UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED

MANAGEMENT INVESTMENT COMPANIES

  Registrant’s telephone number, including area code:          (713) 626-1919      

  Date of fiscal year end:             12/31                

  Date of reporting period:         06/30/21            

ITEM 1. REPORTS TO STOCKHOLDERS.

(a) The Registrant’s semi-annual report transmitted to shareholders pursuant to Rule 30e-1 under the Investment Company Act of 1940 is as follows:

(b) Not Applicable.

For the most current month-end Fund performance and commentary, please visit invesco.com/performance.

Unless otherwise noted, all data provided by Invesco.

This report must be accompanied or preceded by a currently effective Fund prospectus, which contains more complete information, including sales charges and expenses. Investors should read it carefully before investing.

NOT FDIC INSURED  |  MAY LOSE VALUE  |  NO BANK GUARANTEE

Fund Performance

Liquidity Risk Management Program

In compliance with Rule 22e-4 under the Investment Company Act of 1940, as amended (the “Liquidity Rule”), the Fund has adopted and implemented a liquidity risk management program in accordance with the Liquidity Rule (the “Program”). The Program is reasonably designed to assess and manage the Fund’s liquidity risk, which is the risk that the Fund could not meet redemption requests without significant dilution of remaining investors’ interests in the Fund. The Board of Trustees of the Fund (the “Board”) has appointed Invesco Advisers, Inc. (“Invesco”), the Fund’s investment adviser, as the Program’s administrator, and Invesco has delegated oversight of the Program to the Liquidity Risk Management Committee (the “Committee”), which is composed of senior representatives from relevant business groups at Invesco.

As required by the Liquidity Rule, the Program includes policies and procedures providing for an assessment, no less frequently than annually, of the Fund’s liquidity risk that takes into account, as relevant to the Fund’s liquidity risk: (1) the Fund’s investment strategy and liquidity of portfolio investments during both normal and reasonably foreseeable stressed conditions; (2) short-term and long-term cash flow projections for the Fund during both normal and reasonably foreseeable stressed conditions; and (3) the Fund’s holdings of cash and cash equivalents and any borrowing arrangements. The Liquidity Rule also requires the classification of the Fund’s investments into categories that reflect the assessment of their relative liquidity under current market conditions. The Fund classifies its investments into one of four categories defined in the Liquidity Rule: “Highly Liquid,” “Moderately Liquid,” “Less Liquid,” and “Illiquid.” Funds that are not invested primarily in “Highly Liquid Investments” that are assets (cash or investments that are reasonably expected to be convertible into cash within three business days without significantly changing the market value of the investment) are required to establish a “Highly Liquid Investment Minimum” (“HLIM”), which is the minimum percentage of net assets that must be invested in Highly Liquid Investments. Funds with HLIMs have procedures for addressing HLIM shortfalls, including reporting to the Board and the SEC (on a non-public basis) as required by the Program and the Liquidity Rule. In addition, the Fund may not acquire an investment if, immediately after the acquisition, over 15% of the Fund’s net assets would consist of “Illiquid Investments” that are assets (an investment that cannot reasonably be expected to be sold or disposed of in current market conditions in seven calendar days or less without the sale or disposition significantly changing the market value of the investment). The Liquidity Rule and the Program also require reporting to the Board and the SEC (on a non-public basis) if a Fund’s holdings of Illiquid Investments exceed 15% of the Fund’s assets.

At a meeting held on March 22-24, 2021, the Committee presented a report to the Board that addressed the operation of the Program and assessed the Program’s adequacy and effectiveness of implementation (the “Report”). The Report covered the period from January 1, 2020 through December 31, 2020 (the “Program Reporting Period”). The Report discussed notable events affecting liquidity over the Program Reporting Period, including the impact of the coronavirus pandemic on the Fund and the overall market. The Report noted that there were no material changes to the Program during the Program Reporting Period.

The Report stated, in relevant part, that during the Program Reporting Period:

Schedule of Investments

June 30, 2021

(Unaudited)

See accompanying Notes to Financial Statements which are an integral part of the financial statements.

Notes to Schedule of Investments:

Portfolio Composition

By sector, based on Net Assets

as of June 30, 2021

See accompanying Notes to Financial Statements which are an integral part of the financial statements.

Statement of Assets and Liabilities

June 30, 2021

(Unaudited)

See accompanying Notes to Financial Statements which are an integral part of the financial statements.

Statement of Operations

For the six months ended June 30, 2021

(Unaudited)

See accompanying Notes to Financial Statements which are an integral part of the financial statements.

Statement of Changes in Net Assets

For the six months ended June 30, 2021 and the year ended December 31, 2020

(Unaudited)

See accompanying Notes to Financial Statements which are an integral part of the financial statements.

Financial Highlights

(Unaudited)

The following schedule presents financial highlights for a share of the Fund outstanding throughout the periods indicated.

See accompanying Notes to Financial Statements which are an integral part of the financial statements.

Notes to Financial Statements

June 30, 2021

(Unaudited)

NOTE 1–Significant Accounting Policies

Invesco European Small Company Fund (the “Fund”) is a series portfolio of AIM Funds Group (Invesco Funds Group) (the “Trust”). The Trust is a Delaware statutory trust registered under the Investment Company Act of 1940, as amended (the “1940 Act”), as an open-end series management investment company authorized to issue an unlimited number of shares of beneficial interest. Information presented in these financial statements pertains only to the Fund. Matters affecting the Fund or each class will be voted on exclusively by the shareholders of the Fund or each class.

The Fund’s investment objective is long-term growth of capital.

The Fund currently consists of four different classes of shares: Class A, Class C, Class Y and Class R6. Class Y shares are available only to certain investors. Class A shares are sold with a front-end sales charge unless certain waiver criteria are met. Under certain circumstances, load waived shares may be subject to contingent deferred sales charges (“CDSC”). Class C shares are sold with a CDSC. Class Y and Class R6 shares are sold at net asset value. Class C shares held for eight years after purchase are eligible for automatic conversion into Class A shares of the same Fund (the “Conversion Feature”). The automatic conversion pursuant to the Conversion Feature will generally occur at the end of the month following the eighth anniversary after a purchase of Class C shares.

The Fund is an investment company and accordingly follows the investment company accounting and reporting guidance in accordance with Financial Accounting Standards Board Accounting Standards Codification Topic 946, Financial Services – Investment Companies.

The following is a summary of the significant accounting policies followed by the Fund in the preparation of its financial statements.

A security listed or traded on an exchange (except convertible securities) is valued at its last sales price or official closing price as of the close of the customary trading session on the exchange where the security is principally traded, or lacking any sales or official closing price on a particular day, the security may be valued at the closing bid price on that day. Securities traded in the over-the-counter market are valued based on prices furnished by independent pricing services or market makers. When such securities are valued by an independent pricing service they may be considered fair valued. Futures contracts are valued at the final settlement price set by an exchange on which they are principally traded. Listed options are valued at the mean between the last bid and asked prices from the exchange on which they are principally traded. Options not listed on an exchange are valued by an independent source at the mean between the last bid and asked prices. For purposes of determining net asset value (“NAV”) per share, futures and option contracts generally are valued 15 minutes after the close of the customary trading session of the New York Stock Exchange (“NYSE”).

Investments in open-end and closed-end registered investment companies that do not trade on an exchange are valued at the end-of-day net asset value per share. Investments in open-end and closed-end registered investment companies that trade on an exchange are valued at the last sales price or official closing price as of the close of the customary trading session on the exchange where the security is principally traded.

Debt obligations (including convertible securities) and unlisted equities are fair valued using an evaluated quote provided by an independent pricing service. Evaluated quotes provided by the pricing service may be determined without exclusive reliance on quoted prices, and may reflect appropriate factors such as institution-size trading in similar groups of securities, developments related to specific securities, dividend rate (for unlisted equities), yield (for debt obligations), quality, type of issue, coupon rate (for debt obligations), maturity (for debt obligations), individual trading characteristics and other market data. Pricing services generally value debt obligations assuming orderly transactions of institutional round lot size, but a fund may hold or transact in the same securities in smaller, odd lot sizes. Odd lots often trade at lower prices than institutional round lots. Debt obligations are subject to interest rate and credit risks. In addition, all debt obligations involve some risk of default with respect to interest and/or principal payments.

Foreign securities’ (including foreign exchange contracts) prices are converted into U.S. dollar amounts using the applicable exchange rates as of the close of the NYSE. If market quotations are available and reliable for foreign exchange-traded equity securities, the securities will be valued at the market quotations. Because trading hours for certain foreign securities end before the close of the NYSE, closing market quotations may become unreliable. If between the time trading ends on a particular security and the close of the customary trading session on the NYSE, events occur that the investment adviser determines are significant and make the closing price unreliable, the Fund may fair value the security. If the event is likely to have affected the closing price of the security, the security will be valued at fair value in good faith using procedures approved by the Board of Trustees. Adjustments to closing prices to reflect fair value may also be based on a screening process of an independent pricing service to indicate the degree of certainty, based on historical data, that the closing price in the principal market where a foreign security trades is not the current value as of the close of the NYSE. Foreign securities’ prices meeting the approved degree of certainty that the price is not reflective of current value will be priced at the indication of fair value from the independent pricing service. Multiple factors may be considered by the independent pricing service in determining adjustments to reflect fair value and may include information relating to sector indices, American Depositary Receipts and domestic and foreign index futures. Foreign securities may have additional risks including exchange rate changes, potential for sharply devalued currencies and high inflation, political and economic upheaval, the relative lack of issuer information, relatively low market liquidity and the potential lack of strict financial and accounting controls and standards.

Securities for which market prices are not provided by any of the above methods may be valued based upon quotes furnished by independent sources. The last bid price may be used to value equity securities. The mean between the last bid and asked prices is used to value debt obligations, including corporate loans.

Securities for which market quotations are not readily available or became unreliable are valued at fair value as determined in good faith by or under the supervision of the Trust’s officers following procedures approved by the Board of Trustees. Issuer specific events, market trends, bid/asked quotes of brokers and information providers and other market data may be reviewed in the course of making a good faith determination of a security’s fair value.

The Fund may invest in securities that are subject to interest rate risk, meaning the risk that the prices will generally fall as interest rates rise and, conversely, the prices will generally rise as interest rates fall. Specific securities differ in their sensitivity to changes in interest rates depending on their individual characteristics. Changes in interest rates may result in increased market volatility, which may affect the value and/or liquidity of certain Fund investments.

Valuations change in response to many factors including the historical and prospective earnings of the issuer, the value of the issuer’s assets, general market conditions which are not specifically related to the particular issuer, such as real or perceived adverse economic conditions, changes in the general outlook for revenues or corporate earnings, changes in interest or currency rates, regional or global instability, natural or environmental disasters, widespread disease or other public health issues, war, acts of terrorism or adverse investor sentiment generally and market liquidity. Because of the inherent uncertainties of valuation, the values reflected in the financial statements may materially differ from the value received upon actual sale of those investments.

The Fund may periodically participate in litigation related to Fund investments. As such, the Fund may receive proceeds from litigation settlements. Any proceeds received are included in the Statement of Operations as realized gain (loss) for investments no longer held and as unrealized gain (loss) for investments still held.

Brokerage commissions and mark ups are considered transaction costs and are recorded as an increase to the cost basis of securities purchased and/or a reduction of proceeds on a sale of securities. Such transaction costs are included in the determination of net realized and unrealized gain (loss) from investment securities reported in the Statement of Operations and the Statement of Changes in Net Assets and the net realized and unrealized gains (losses) on securities per share in the Financial Highlights. Transaction costs are included in the calculation of the Fund’s net asset value and, accordingly, they reduce the Fund’s total returns. These transaction costs are not considered operating expenses and are not reflected in net investment income reported in the Statement of Operations and the Statement of Changes in Net Assets, or the net investment income per share and the ratios of expenses and net investment income reported in the Financial Highlights, nor are they limited by any expense limitation arrangements between the Fund and the investment adviser.

The Fund allocates income and realized and unrealized capital gains and losses to a class based on the relative net assets of each class.

The Fund recognizes the tax benefits of uncertain tax positions only when the position is more likely than not to be sustained. Management has analyzed the Fund’s uncertain tax positions and concluded that no liability for unrecognized tax benefits should be recorded related to uncertain tax positions. Management is not aware of any tax positions for which it is reasonably possible that the total amounts of unrecognized tax benefits will change materially in the next 12 months.

The Fund files tax returns in the U.S. Federal jurisdiction and certain other jurisdictions. Generally, the Fund is subject to examinations by such taxing authorities for up to three years after the filing of the return for the tax period.

The Fund may invest in foreign securities, which may be subject to foreign taxes on income, gains on investments or currency repatriation, a portion of which may be recoverable. Foreign taxes, if any, are recorded based on the tax regulations and rates that exist in the foreign markets in which the Fund invests and are shown in the Statement of Operations.

The Fund may also enter into forward foreign currency contracts for the purchase or sale of a security denominated in a foreign currency in order to “lock in” the U.S. dollar price of that security, or the Fund may also enter into forward foreign currency contracts that do not provide for physical settlement of the two currencies, but instead are settled by a single cash payment calculated as the difference between the agreed upon exchange rate and the spot rate at settlement based upon an agreed upon notional amount (non-deliverable forwards). The Fund will set aside liquid assets in an amount equal to the daily mark-to-market obligation for forward foreign currency contracts.

A forward foreign currency contract is an obligation between two parties (“Counterparties”) to purchase or sell a specific currency for an agreed-upon price at a future date. The use of forward foreign currency contracts does not eliminate fluctuations in the price of the underlying securities the Fund owns or intends to acquire but establishes a rate of exchange in advance. Fluctuations in the value of these contracts are measured by the difference in the contract date and reporting date exchange rates and are recorded as unrealized appreciation (depreciation) until the contracts are closed. When the contracts are closed, realized gains (losses) are recorded. Realized and unrealized gains (losses) on the contracts are included in the Statement of Operations. The primary risks associated with forward foreign currency contracts include failure of the Counterparty to meet the terms of the contract and the value of the foreign currency changing unfavorably. These risks may be in excess of the amounts reflected in the Statement of Assets and Liabilities.

The ongoing effects of COVID-19 are unpredictable and may result in significant and prolonged effects on the Fund’s performance.

NOTE 2–Advisory Fees and Other Fees Paid to Affiliates

The Trust has entered into a master investment advisory agreement with Invesco Advisers, Inc. (the “Adviser” or “Invesco”). Under the terms of the investment advisory agreement, the Fund accrues daily and pays monthly an advisory fee to the Adviser based on the annual rate of the Fund’s average daily net assets as follows:

For the six months ended June 30, 2021, the effective advisory fee rate incurred by the Fund was 0.93%.

Under the terms of a master sub-advisory agreement between the Adviser and each of Invesco Asset Management Deutschland GmbH, Invesco Asset Management Limited, Invesco Asset Management (Japan) Limited, Invesco Hong Kong Limited, Invesco Senior Secured Management, Inc. and Invesco Canada Ltd. and separate sub-advisory agreements with Invesco Capital Management LLC and Invesco Asset Management (India) Private Limited (collectively, the “Affiliated Sub-Advisers”) the Adviser, not the Fund, will pay 40% of the fees paid to the Adviser to any such Affiliated Sub-Adviser(s) that provide(s) discretionary investment management services to the Fund based on the percentage of assets allocated to such Affiliated Sub-Adviser(s).

The Adviser has contractually agreed, through at least June 30, 2022, to waive advisory fees and/or reimburse expenses of all shares to the extent necessary to limit total annual fund operating expenses after fee waiver and/or expense reimbursement (excluding certain items discussed below) of Class A, Class C, Class Y and Class R6 shares to 2.25%, 3.00%, 2.00% and 2.00%, respectively, of the Fund’s average daily net assets (the “expense limits”). In determining the Adviser’s obligation to waive advisory fees and/or reimburse expenses, the following expenses are not taken into account, and could cause the total annual fund operating expenses after fee waiver and/or expense reimbursement to exceed the numbers reflected above: (1) interest; (2) taxes; (3) dividend expense on short sales; (4) extraordinary or non-routine items, including litigation expenses; and (5) expenses that the Fund has incurred but did not actually pay because of an expense offset arrangement. Unless Invesco continues the fee waiver agreement, it will terminate on June 30, 2022. During its term, the fee waiver agreement cannot be terminated or amended to increase the expense limits or reduce the advisory fee waiver without approval of the Board of Trustees. The Adviser did not waive fees and/or reimburse expenses during the period under these expense limits.

Further, the Adviser has contractually agreed, through at least June 30, 2023, to waive the advisory fee payable by the Fund in an amount equal to 100% of the net advisory fees the Adviser receives from the affiliated money market funds on investments by the Fund of uninvested cash (excluding investments of cash collateral from securities lending) in such affiliated money market funds.

For the six months ended June 30, 2021, the Adviser waived advisory fees of $4,019.

The Trust has entered into a master administrative services agreement with Invesco pursuant to which the Fund has agreed to pay Invesco for certain administrative costs incurred in providing accounting services to the Fund. For the six months ended June 30, 2021, expenses incurred under the agreement are shown in the Statement of Operations as Administrative services fees. Invesco has entered into a sub-administration agreement whereby State Street Bank and Trust Company (“SSB”) serves as fund accountant and provides certain administrative services to the Fund. Pursuant to a custody agreement with the Trust on behalf of the Fund, SSB also serves as the Fund’s custodian.

The Trust has entered into a transfer agency and service agreement with Invesco Investment Services, Inc. (“IIS”) pursuant to which the Fund has agreed to pay IIS a fee for providing transfer agency and shareholder services to the Fund and reimburse IIS for certain expenses incurred by IIS in the course of providing such services. IIS may make payments to intermediaries that provide omnibus account services, sub-accounting services and/or networking services. All fees payable by IIS to intermediaries that provide omnibus account services or sub-accounting services are charged back to the Fund, subject to certain limitations approved by the Trust’s Board of Trustees. For the six months ended June 30, 2021, expenses incurred under the agreement are shown in the Statement of Operations as Transfer agent fees.

The Trust has entered into master distribution agreements with Invesco Distributors, Inc. (“IDI”) to serve as the distributor for the Class A, Class C, Class Y and Class R6 shares of the Fund. The Trust has adopted plans pursuant to Rule 12b-1 under the 1940 Act with respect to the Fund’s Class A and Class C shares (collectively, the “Plans”). The Fund, pursuant to the Plans, pays IDI compensation at the annual rate of 0.25% of the Fund’s average daily net assets of Class A shares and 1.00% of the average daily net assets of Class C shares. The fees are accrued daily and paid monthly. Of the Plan payments, up to 0.25% of the average daily net assets of each class of shares may be paid to furnish continuing personal shareholder services to customers who purchase and own shares of such classes. Any amounts not paid as a service fee under the Plans would constitute an asset-based sales charge. Rules of the Financial Industry Regulatory Authority (“FINRA”) impose a cap on the total sales

charges, including asset-based sales charges, that may be paid by any class of shares of the Fund. For the six months ended June 30, 2021, expenses incurred under the Plans are shown in the Statement of Operations as Distribution fees.

Front-end sales commissions and CDSC (collectively, the “sales charges”) are not recorded as expenses of the Fund. Front-end sales commissions are deducted from proceeds from the sales of Fund shares prior to investment in Class A shares of the Fund. CDSC are deducted from redemption proceeds prior to remittance to the shareholder. During the six months ended June 30, 2021, IDI advised the Fund that IDI retained $2,609 in front-end sales commissions from the sale of Class A shares and $8 and $6 from Class A and Class C shares, respectively, for CDSC imposed upon redemptions by shareholders.

For the six months ended June 30, 2021, the Fund incurred $277 in brokerage commissions with Invesco Capital Markets, Inc., an affiliate of the Adviser and IDI, for portfolio transactions executed on behalf of the Fund.

Certain officers and trustees of the Trust are officers and directors of the Adviser, IIS and/or IDI.

NOTE 3–Additional Valuation Information

GAAP defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date, under current market conditions. GAAP establishes a hierarchy that prioritizes the inputs to valuation methods, giving the highest priority to readily available unadjusted quoted prices in an active market for identical assets (Level 1) and the lowest priority to significant unobservable inputs (Level 3), generally when market prices are not readily available or are unreliable. Based on the valuation inputs, the securities or other investments are tiered into one of three levels. Changes in valuation methods may result in transfers in or out of an investment’s assigned level:

The following is a summary of the tiered valuation input levels, as of June 30, 2021. The level assigned to the securities valuations may not be an indication of the risk or liquidity associated with investing in those securities. Because of the inherent uncertainties of valuation, the values reflected in the financial statements may materially differ from the value received upon actual sale of those investments.

NOTE 4–Trustees’ and Officers’ Fees and Benefits

Trustees’ and Officers’ Fees and Benefits include amounts accrued by the Fund to pay remuneration to certain Trustees and Officers of the Fund. Trustees have the option to defer compensation payable by the Fund, and Trustees’ and Officers’ Fees and Benefits also include amounts accrued by the Fund to fund such deferred compensation amounts. Those Trustees who defer compensation have the option to select various Invesco Funds in which their deferral accounts shall be deemed to be invested. Finally, certain current Trustees were eligible to participate in a retirement plan that provided for benefits to be paid upon retirement to Trustees over a period of time based on the number of years of service. The Fund may have certain former Trustees who also participate in a retirement plan and receive benefits under such plan. Trustees’ and Officers’ Fees and Benefits include amounts accrued by the Fund to fund such retirement benefits. Obligations under the deferred compensation and retirement plans represent unsecured claims against the general assets of the Fund.

NOTE 5–Cash Balances

The Fund is permitted to temporarily carry a negative or overdrawn balance in its account with SSB, the custodian bank. Such balances, if any at period-end, are shown in the Statement of Assets and Liabilities under the payable caption Amount due custodian. To compensate the custodian bank for such overdrafts, the overdrawn Fund may either (1) leave funds as a compensating balance in the account so the custodian bank can be compensated by earning the additional interest; or (2) compensate by paying the custodian bank at a rate agreed upon by the custodian bank and Invesco, not to exceed the contractually agreed upon rate. The Fund may not purchase additional securities when any borrowings from banks or broker-dealers exceed 5% of the Fund’s total assets, or when any borrowings from an Invesco Fund are outstanding.

NOTE 6–Tax Information

The amount and character of income and gains to be distributed are determined in accordance with income tax regulations, which may differ from GAAP. Reclassifications are made to the Fund’s capital accounts to reflect income and gains available for distribution (or available capital loss carryforward) under income tax regulations. The tax character of distributions paid during the year and the tax components of net assets will be reported at the Fund’s fiscal year-end.

Capital loss carryforward is calculated and reported as of a specific date. Results of transactions and other activity after that date may affect the amount of capital loss carryforward actually available for the Fund to utilize. The ability to utilize capital loss carryforwards in the future may be limited under the Internal Revenue Code and related regulations based on the results of future transactions.

The Fund had a capital loss carryforward as of December 31, 2020, as follows:

NOTE 7–Investment Transactions

The aggregate amount of investment securities (other than short-term securities, U.S. Government obligations and money market funds, if any) purchased and sold by the Fund during the six months ended June 30, 2021 was $1,726,103 and $26,539,144, respectively. Cost of investments, including any derivatives, on a tax basis includes the adjustments for financial reporting purposes as of the most recently completed federal income tax reporting period-end.

Cost of investments for tax purposes is $180,847,791.

NOTE 8–Share Information