The basis for this book is a number of lectures given frequently by the author to third year students of the Department of Economics at Leningrad State University who specialize in economical cybernetics. The main purpose of this book is to provide the student with a relatively simple and easy-to-understand manual containing the basic mathematical machinery utilized in the theory of games. Practical examples (including those from the field of economics) serve mainly as an interpretation of the mathematical foundations of this theory rather than as indications of their actual or potential applicability. The present volume is significantly different from other books on the theory of games. The difference is both in the choice of mathematical problems as well as in the nature of the exposition. The realm of the problems is somewhat limited but the author has tried to achieve the greatest possible systematization in his exposition. Whenever possible the author has attempted to provide a game-theoretical argument with the necessary mathematical rigor and reasonable generality. Formal mathematical prerequisites for this book are quite modest. Only the elementary tools of linear algebra and mathematical analysis are used.