American mathematician R. Bellman is known to the Soviet reader for the translation of two of his books ("The Theory of Stability of Solutions of Differential Equations, IL, 1954; "Dynamic Programming", IL, I960). This work, written by him together with his colleagues, is devoted to various mathematical methods used in the theory of management processes. The authors consistently describe the diverse mathematical means of solving a general problem of optimal control of a system. To solve this problem, the theory of differential, difference and functional equations, classical and modern methods of variational calculus, the theory of linear spaces, the theory of dynamic programming and game theory are used. The book is of interest to scientists and engineers dealing with problems of optimal management in engineering, economics, etc. d. as well as for mathematicians of various specialties.