Elements of the theory of sets

This brochure is a notes of the course on the elementary theory of sets, which the professor of Moscow State University O. V. Lokutsievsky read in the 60s of the last century students of the eighth (in the modern numbering-nine) class of the Moscow Mathematical School number 2. Oleg Vyacheslavovich was an outstanding mathematician and wonderful man. His work was associated with two large mathematically centers-mechanical-mathematics faculty of Moscow University and the Department of Applied Mathematics (now the Institute of Applied Mathematics named after M.V. Keldysh) The second school - an outstanding physical and mathematical school of that time - raised many brilliant scientists in its walls. For high school students interested in mathematics and teachers working in mathematical schools