To obtain the subject copolymer having a high glass transition point, by copolymerizing an α-olefin with a specific norbornene in the presence of a prescribed catalyst and specifying a glass transition point, etc.

(A) An 2-20C α-olefin is copolymerized with (B) a norbornene of formula I (R1 to R8 are each H, a halogen or a hydrocarbon and R5 is bonded to R6 and R7 is bonded to R8 to form an alkylidene) in the presence of (C) (i) a transition metal compound of formula II [M is Ti, Zr or the like; R11 and R12 are each a (substituted) indenyl or the like; R13 and R14 are each a 1-10C alkyl a 6-10C aryl or the like; X1 and X2 are each an O-containing group, H or the like], (ii) an organoaluminum oxy compound and /or a compound which is reacted with the component (i) to form a counter ion and (iii) optionally an organoaluminum compound to give the objective copolymer containing ≥60 mol.% of a constituent unit derived from the component B and having ≥160°C glass transition point.