The present invention relates to a polar group-containing olefin copolymer (A) which is produced through polymerization using a transition metal catalyst, which has a weight-average molecular weight falling within a specific range and which contains a polar group-containing monomer within a specific range; a multinary polar olefin copolymer (A) indispensably containing a polar monomer component that has a norbornene skeleton and a carboxyl group or an acid anhydride group and having three or more types of monomer units; and a resin composition (C) containing a specific amount of a polar group-containing olefin copolymer (A) and a specific amount of an olefin resin (B).