The present invention provides a copolymer which can prevent problems associated with immersion lithography (including occurrence of a pattern defect such as water mark, and variation in sensitivity or abnormal patterning due to elution of an additive such as a radiation-sensitive acid-generator) and which provides surface characteristics suitable for immersion lithography, and a composition containing the copolymer.The copolymer for immersion lithography has, at least, a repeating unit (A) that generates an alkali-soluble group by removing protecting group through action of an acid, and a repeating unit (B) having a lactone structure, wherein, when a solution of the copolymer in propylene glycol monomethyl ether acetate (hereinafter may be abbreviated as “PGMEA”) is applied to a wafer and then heated to form a thin film, and a 15-μL droplet of pure water is added onto the thin film, the inclination of the wafer at the time when the water droplet starts to move is 35° or less, or the contact angle of the top edge of the water droplet at the time when the water droplet starts to move is 64° or more.