This method for manufacturing a polymer includes a step for preparing a precursor polymer including structural units represented by formula (1a), a step for applying water or an alcohol represented by the formula R1-OH (where R1 is a C1-18 organic group) to the precursor polymer including structural units represented by formula (1a) to cause ring opening of maleic anhydride portions of the structural units represented by formula (1a) and generating a carboxyl group or a salt thereof in the precursor polymer, and a step for reacting a compound provided with an epoxy group represented by formula (3) with the precursor polymer in which maleic anhydride portions are ring-opened. (In formula (3), R2 represents a C2-18 organic group and has a carbon-carbon double bond in the structure thereof.)