A copolymer formed by the ring-opening metathesis polymerization of a cycloolefinic monomer having a carboxylic anhydride group selected among cycloheptene derivatives, tetracyclododecene derivatives, and hexacycloheptadecene derivatives with a cycloolefinic monomer selected among bicycloheptene derivatives, bicycloheptene derivatives, tetracyclododecene derivatives, and hexacycloheptadecene derivatives; and a product of hydrogenation of the copolymer. In producing the copolymer, a polymerization catalyst is used which comprises an organoruthenium compound having a heterocyclic carbene compound as a ligand. The copolymer and the hydrogenated copolymer are reduced in permittivity and water absorption, have high adhesion to metals, and have excellent heat resistance.