The present invention relates to a copolymer including a monomer unit (a) derived from a conjugated diene having not more than 12 carbon atoms and a monomer unit (b) derived from farnesene; a process for producing the copolymer including at least the step of copolymerizing a conjugated diene having not more than 12 carbon atoms with farnesene; a rubber composition including (A) the copolymer, (B) a rubber component and (C) carbon black; a rubber composition including (A) the copolymer, (B) a rubber component and (D) silica; a rubber composition including (A) the copolymer, (B) a rubber component, (C) carbon black and (D) silica; and a tire using the rubber composition at least as a part thereof.