Igumnov studied under Nikolai Zverev, and at Moscow Conservatory under Alexander Siloti and Pavel Pabst.

He took theory and composition courses from Sergei Taneyev, Anton Arensky and Mikhail Ippolitov-Ivanov.

[1] Among his many students were Arno Babajanian, Bolesław Kon, Naum Shtarkman, Elena Beckman-Shcherbina, Yakov Flier, Boris Berlin, Lev Oborin, Maria Grinberg, Andrzej Wasowski, Elena Laumenskienė, Ryszard Bakst, Tengiz Amirejibi, Anatoly Alexandrov, Bella Davidovich, Rosa Tamarkina, Issay Dobrowen, and Mariya Gambaryan.

[citation needed] Igumnov was evacuated to Yerevan, Armenia during the first half of 1940s.

A four-record (LP) set of Igumnov's recordings was issued by Melodiya on 33C 10-05519-26.