The invention provides a polymer comprising recurring units containing bridged aliphatic rings in the backbone and having a hydroxyl, acyloxy or alkoxylcarbonyloxy group as well as a lactone structure bonded through a spacer, the polymer having a weight average molecular weight of 1,000-500,000. A resist composition comprising the polymer as a base resin is sensitive to high-energy radiation, has excellent sensitivity, resolution, and etching resistance, and lends itself to micropatterning with electron beams or deep-UV.