Using a system of entertaining problems, the book reveals the mathematical foundations of the theory of automata and considers its application to solve problems arising in various fields of science, technology and production. Considerable attention is paid to the algebra of logic and graph theory, the mastery of which is inherent in the successful compilation of algorithms and computer programs. Historical information and brief biographies of scientists whose names are associated with the issues considered in the book are given. The publication is illustrated. Intended for high school students.