A low-molecular-weight polyester resin which can elasticize a resin suitably and can be used for various purposes, various resins obtained by using the resin, and the purposes thereof. The polyester resin is obtained by polymerizing a monomer composition containing 10 to 90 weight % of a linear dicarboxylic acid and/or diol having at least 8 carbon atoms (I), 5 to 80 weight % of a branched dicarboxylic acid and/or diol having at least 4 carbon atoms (II-1) and/or 2 to 40 weight % of at least one polyfunctional monomer (II-2) selected from the group consisting of polyols, polycarboxylic acids and hydroxycarboxylic acids having 3 or more functional groups respectively and which has the number average molecular weight of 500 to 5000 and is amorphous.