Exhibit 4.1

FIRST AMENDMENT TO COMMON STOCK PURCHASE WARRANT

THIS FIRST AMENDMENT TO COMMON STOCK PURCHASE WARRANT (this “First Amendment”), dated as of December 20, 2018 (the “Amendment Date”), is entered into by and between Richard E. Uihlein, an individual resident of the State of Illinois (hereinafter the “Holder”), and Galectin Therapeutics, Inc., a Nevada corporation (hereinafter the “Company”). The Holder and the Company shall each be referred to herein individually as a “Party” and, collectively, as the “Parties.”

RECITALS

WHEREAS, the Company issued that certain Common Stock Purchase Warrant to the Holder on December 19, 2017 (the “Warrant”); and

WHEREAS, the Parties wish to amend the Warrant in accordance with the terms of Section 10.2 thereof to reflect certain changes as set forth herein.

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties agree as follows:

1.    Amendment to Preamble to the Warrant. The preamble to the Warrant is hereby amended by deleting the phrase “. . .dated as of December     , 2017 . . .” and inserting the following in lieu thereof: “. . .dated as of December 19, 2017 . . .”

2.    Amendment to Definition of “Issue Date”. Section 1 of the Warrant (Definitions) is hereby amended by deleting the definition of “Issue Date” in its entirety and inserting the following in lieu thereof: ““Issue Date” means December 19, 2017.”

3.    Amendment to Section 2.1 of the Warrant. Section 2.1 of the Warrant (Vesting) is hereby amended by deleting all references to “December 31, 2018” contained therein and inserting the following in lieu thereof: “December 31, 2019”.

4.    Miscellaneous. Except as amended by this First Amendment, the Warrant remains in full force and effect in accordance with its terms. This First Amendment shall be governed by and interpreted in accordance with the laws of the State of Nevada. If any provision of this First Amendment or part thereof is rendered void, illegal or unenforceable in any respect under any applicable law, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby. This First Amendment may only be amended in the same manner as the Warrant. Capitalized terms used herein without specific definition have the respective meanings given to them in the Warrant. This First Amendment may be executed in counterparts, each of which shall be deemed to be an original; provided, however, that such counterparts shall together constitute only one instrument. A signed copy of this First Amendment transmitted by facsimile, email or other means of electronic transmission shall be deemed to have the same legal effect as delivery of an original executed copy of this First Amendment for all purposes.

[Signatures Appear on the Following Page]

IN WITNESS WHEREOF, the Parties have duly authorized and executed this First Amendment as of the Amendment Date.

By:	/s/ Richard E. Uihlein
	Richard E. Uihlein
GALECTIN THERAPEUTICS, INC.
By:	/s/ Harold H. Shlevin
Name:	Harold H. Shlevin
Title:	Chief Executive Officer