Silvestrov began private music lessons when he was 15. After first teaching himself, he studied piano at the Kyiv Evening Music School from 1955 to 1958 whilst at the same time training to become a civil engineer. He attended the Kyiv Conservatory from 1958 to 1964, where he was taught musical composition by Borys Lyatoshynsky, and harmony and counterpoint by Levko Revutsky. He then taught at a music studio in Kyiv.
