(54) Title: UV ABSORBING COMPLEX POLYESTER POLYMERS, COMPOSITIONS CONTAINING UV ABSORBING COMPLEX POLYESTER POLYMERS, AND RELATED METHODS (57) Abstract: A UV absorbing complex polyol polyester polymer is the product of a reaction scheme that includes: (i) the esterification of a polyol and a dianhydride, wherein the esterification is carried out under conditions that facilitate substantially only anhydride opening, to form a polyester polymer comprising at least two pendant carboxylic groups, and at least two hy-droxyl groups: and (ii) the reaction of at least one pendant carboxylic group and at least one terminal hydroxyl group of the polyester polymer with an epoxide having a functional group, wherein the epoxide comprises an UV absorbing moiety. A crosslinked UV absorbing complex polyol polyester polymer that is reaction product of a random copolyesterification esterification reaction and/or the esterification product.