Klimov was born on October 16, 1931 in
Kyiv (then in the
Soviet Union, now in
Ukraine). He began to study music under the guidance of his father - conductor and teacher . From the age of 7 (with a break for evacuation in Stalingrad during the war) he studied at the Odessa Music Boarding School for Gifted Children with
Pyotr Stolyarsky (now called the
School of Stolyarsky). Starting in 1945, he studied with B.Z. Mordkovich. In 1949 he performed public concerts featuring repertoire by
Alexander Glazunov,
W.A. Mozart and
Felix Mendelssohn. There he met
David Oistrakh whom he studied with at the
Moscow Conservatory. ==Awards and titles==