Born in Brno, Czechoslovakia, on April 1, 1929. His father, the musicologist and pianist Ludvík Kundera (1891-1971), was director of the Academy of Music. After the Second World War, Kundera joined the Communist Party, which was ousted after the events of 1948. He had to make a living from various occupations, particularly as a jazz pianist, an instrument that his father had taught him to play at an early age.