Rudin was born in 1960, in Moscow, and he studied piano and cello at the Gnessin Institute before later studying conducting at the Moscow Conservatory with Dmitri Kitayenko. He has won prizes in many international competitions, and has performed as a solo cellist with such orchestras as the Royal Philharmonic, the Vienna Symphony and the Danish Radio Orchestras. His interest in authentic performance practice has led him to play early music and baroque music on both the cello and viola da gamba, in "historically correct" manner.