The present book contains 350 problems selected from the material of the mathematical olympiads and school mathematics hobby groups in Moscow. About 15 problems have been taken from the manuscript of the late D. O. Shklyarsky (1918-1942), one of the founders of the mathematics hobby group for pupils at the State University of Moscow.
It is a great pleasure to thank I. Bernstein, N. Vasilyev. G. Galperin, Yu. Ionin, A. Leman, A. Savin, A. Tolpygo, A. Toom, V. Gutenmacher, L. Макаг-Limanov and L. I. Golovina for valuable advice and help in the preparation of the book.