Exhibit 10.1 

APTORUM GROUP LIMITED

17 Hanover Square

London, XO W1S 1BN

United Kingdom

Holder of Class A Ordinary Shares Purchase Warrant

Re: Exchange Offer of Class A Ordinary Shares Purchase Warrant

Dear Holder:

Aptorum Group Limited (the “Company”) is pleased to offer to you the opportunity to exchange all of the Class A Ordinary Shares Purchase Warrants (the “Exchange Warrants”) currently held by you (the “Holder”) into shares of Common Stock. Capitalized terms not otherwise defined herein shall have the meanings set forth in the Securities Purchase Agreement, dated as of February __, 2020, between the Company and the purchasers signatory thereto pursuant to which the Company issued the Exchange Warrants.

In consideration for exchanging in full all of the Exchange Warrants held by you (the “Warrant Exchange”), the Company hereby offers you in exchange therefor 1.0 shares of Common Stock (“Exchange Shares”) for each Warrant Share being exchanged. Notwithstanding anything herein to the contrary, in the event that the Warrant Exchange would cause the Holder to exceed the Beneficial Ownership Limitation (as defined in the Exchange Warrant) in the Exchange Warrant, the Company shall only issue such number of shares of Common Stock to the Holder that would not cause the Holder to exceed the Beneficial Ownership Limitation with the balance to be held in abeyance until written notice from the Holder that the balance (or portion thereof) may be issued in compliance with the Beneficial Ownership Limitation, which abeyance shall be evidenced through the Existing Warrant which shall be deemed prepaid thereafter, and exercised pursuant to a Notice of Exercise in the Exchange Warrant (provided no additional exercise shall be payable and any rights of adjustment or termination thereunder Other than Section 3(a) thereunder shall have no force or effect). The Company agrees that the Warrant Exchange shall in no event result in the Holder beneficially owning more than the Beneficial Ownership Limitation. Within two Trading Days of the date hereof, the Company shall deliver the Exchange Shares to the DTC account of the Holder via the DWAC system. The terms of the Exchange Warrant, including but not limited to the obligations to deliver the Exchange Shares, shall remain in effect as if the acceptance of this offer was a formal Notice of Exercise of a cashless exercise to receive the Exchange Shares (including but not limited to any liquidated damages and compensation in the event of late delivery of the Exchange Shares).

The Exchange Shares are being issued in a cashless exchange for the Exchange Warrants and the parties acknowledge and agree that in accordance with Section 3(a)(9) of the Securities Act, the Exchange Shares shall take on the registered characteristics of the Exchange Warrants.  The Company agrees not to take any position contrary to this Section 2(c).

Additionally, the Company and the Holder hereby agree to amend and restate Section 4.11 of the Purchase Agreement as follows (which amendment shall only become effective upon agreement to amend by all Purchasers under the Purchase Agreement): 

Expressly subject to the paragraph immediately following this paragraph below, Holder may accept this offer by signing this letter below, with such acceptance constituting Holder's exchange in full of the Exchange Warrant for Exchange Shares, subject to the Beneficial Ownership Limitation on or before 8:00 a.m. (New York City time) on August ___, 2020.

Additionally, the Company agrees to the representations, warranties and covenants set forth on Annex A attached hereto.

Other than an Exempt Issuance (as defined in the Purchase Agreement), from the date hereof until 15 days following the date hereof, (i) the Company and each Subsidiary shall not issue, enter into any agreement to issue or announce the issuance or proposed issuance of any shares of Common Stock or any securities convertible or exchangeable into Common Stock and (ii) the Company shall not enter into any agreement to amend, exchange or otherwise provide any incentive to exercise any of the warrants originally issued together with the Exchange Warrant or any other warrants of the Company that are outstanding on the date hereof.

On or before 9:00 a.m. (New York City time) on August __, 2020, the Company shall file a Current Report on Form 6-K with the Securities and Exchange Commission disclosing all material terms of the transactions contemplated hereunder, including this agreement as an exhibit thereto (“6-K Filing”). From and after the issuance of the 6-K Filing, the Company represents to the Holder that it shall not be in possession of any material, nonpublic information received from the Company, any of its Subsidiaries or any of their respective officers, directors, employees or agents, that is not disclosed in the 6-K Filing. In addition, effective upon the filing of the 6-K Filing, the Company acknowledges and agrees that any and all confidentiality or similar obligations under any agreement, whether written or oral, between the Company, any of its Subsidiaries or any of their respective officers, directors, employees or agents, on the one hand, and the Holder or any of its affiliates, on the other hand, shall terminate. The Company shall not, and shall cause each of its Subsidiaries and its and each of their respective officers, directors, employees and agents, not to, provide the Holder with any material, nonpublic information regarding the Company or any of its Subsidiaries from and after the date hereof without the express prior written consent of the Holder. To the extent that the Company, any of its Subsidiaries or any of their respective officers, directors, employees or agents, delivers any material, non-public information to the Holder without the Holder’s consent, the Company hereby covenants and agrees that the Holder shall not have any duty of confidentiality with respect to, or a duty not to trade on the basis of, such material, non-public information.

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The Company acknowledges and agrees that the obligations of the Holder under this letter agreement are several and not joint with the obligations of any other holder of Common Stock purchase warrants of the Company (each, an “Other Holder”) under any other agreement related to the exercise of such warrants (“Other Warrant Exchange Agreement”), and the Holder shall not be responsible in any way for the performance of the obligations of any Other Holder or under any such Other Warrant Exchange Agreement. Nothing contained in this letter agreement, and no action taken by the Holder pursuant hereto, shall be deemed to constitute the Holder and the Other Holders as a partnership, an association, a joint venture or any other kind of entity, or create a presumption that the Holder and the Other Holders are in any way acting in concert or as a group with respect to such obligations or the transactions contemplated by this letter agreement and the Company acknowledges that the Holder and the Other Holders are not acting in concert or as a group with respect to such obligations or the transactions contemplated by this letter agreement or any Other Warrant Exchange Agreement. The Company and the Holder confirm that the Holder has independently participated in the negotiation of the transactions contemplated hereby with the advice of its own counsel and advisors. The Holder shall be entitled to independently protect and enforce its rights, including, without limitation, the rights arising out of this letter agreement, and it shall not be necessary for any Other Holder to be joined as an additional party in any proceeding for such purpose.

The Company hereby represents and warrants as of the date hereof and covenants and agrees from and after the date hereof until the three (3) month anniversary of the date hereof that none of the terms offered to any Other Holder with respect to any Other Warrant Exchange Agreement (or any amendment, modification or waiver thereof), is or will be more favorable to such Other Holder than those of the Holder and this letter agreement. If and whenever on or after the date hereof, the Company enters into an Other Warrant Exchange Agreement, then (i) the Company shall provide notice thereof to the Holder promptly following the occurrence thereof and (ii) the terms and conditions of this letter agreement shall be, without any further action by the Holder or the Company, automatically amended and modified in an economically and legally equivalent manner such that the Holder shall receive the benefit of the more favorable terms and/or conditions (as the case may be) set forth in such Other Warrant Exchange Agreement (or any amendment, modification or waiver to this or the Purchase Agreement, including the issuance of additional Exchange Shares or the issuance of new Common Stock purchase warrants to the Other Holder), including, without limitation, the same price discount and the same issuance of new warrants as in the Other Warrant Exchange Agreement, provided that upon written notice to the Company at any time the Holder may elect not to accept the benefit of any such amended or modified term or condition, in which event the term or condition contained in this letter agreement shall apply to the Holder as it was in effect immediately prior to such amendment or modification as if such amendment or modification never occurred with respect to the Holder. The provisions of this paragraph shall apply similarly and equally to each Other Warrant Exchange Agreement.

Except as expressly set forth herein, each party shall pay the fees and expenses of its advisers, counsel, accountants and other experts, if any, and all other expenses incurred by such party incident to the negotiation, preparation, execution, delivery and performance of this letter agreement. The Company shall pay all transfer agent fees, stamp taxes and other taxes and duties levied in connection with the delivery of any Exchange Shares. This letter agreement shall be governed by the laws of the State of New York without regard to the principles of conflicts of law thereof.

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To accept this offer, Holder must counter execute this letter agreement and return the fully executed agreement to the Company at e-mail: ________, attention: _______, on or before 8:00 am (New York City time) on August ___, 2020.

Please do not hesitate to call me if you have any questions.

Sincerely yours,

APTORUM GROUP LIMITED

By:

Name:

Title:

Accepted and Agreed to:

Name of Holder: ___________________________________________________________

Signature of Authorized Signatory of Holder: ____________________________________

Name of Authorized Signatory: _______________________________________________

Title of Authorized Signatory: ________________________________________________

Exchange Warrant Shares: _____________________

Exchange Shares: _____________________

DTC Instructions:

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Annex A

Representations, Warranties and Covenants of the Company. The Company hereby makes the following representations and warranties to the Holder:

(a) Authorization; Enforcement. The Company has the requisite corporate power and authority to enter into and to consummate the transactions contemplated by this letter agreement and otherwise to carry out its obligations hereunder and thereunder. The execution and delivery of this Agreement by the Company and the consummation by the Company of the transactions contemplated hereby have been duly authorized by all necessary action on the part of the Company and no further action is required by the Company, its board of directors or its stockholders in connection therewith. This letter agreement has been duly executed by the Company and, when delivered in accordance with the terms hereof, will constitute the valid and binding obligation of the Company enforceable against the Company in accordance with its terms, except (i) as limited by general equitable principles and applicable bankruptcy, insolvency, reorganization, moratorium and other laws of general application affecting enforcement of creditors’ rights generally, (ii) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies and (iii) insofar as indemnification and contribution provisions may be limited by applicable law.

(b) No Conflicts. The execution, delivery and performance of this letter agreement by the Company and the consummation by the Company of the transactions contemplated hereby do not and will not: (i) conflict with or violate any provision of the Company’s certificate or articles of incorporation, bylaws or other organizational or charter documents; or (ii) conflict with, or constitute a default (or an event that with notice or lapse of time or both would become a default) under, result in the creation of any Lien upon any of the properties or assets of the Company in connection with, or give to others any rights of termination, amendment, acceleration or cancellation (with or without notice, lapse of time or both) of, any material agreement, credit facility, debt or other material instrument (evidencing Company debt or otherwise) or other material understanding to which such Company is a party or by which any property or asset of the Company is bound or affected; or (iii) conflict with or result in a violation of any law, rule, regulation, order, judgment, injunction, decree or other restriction of any court or governmental authority to which the Company is subject (including federal and state securities laws and regulations), or by which any property or asset of the Company is bound or affected.

(c) Nasdaq Corporate Governance. The transactions contemplated under this letter agreement, comply with all rules of the Nasdaq Stock Market.

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