The book discusses the basic concepts and methodological principles of operations research, mathematical methods of optimization (linear, dynamic programming, game theory and statistical solutions), as well as methods of mathematical modeling of operations .. Much attention is paid to the applied theory of Markov random processes (with applications in the field of mass service theory, reliability theory) and the mathematical description of processes occurring in complex, multi-element systems (the method of medium dynamics). Methods of statistical modeling of ECM operations and the basics of the method of network planning are considered . The presentation is conducted at a level that is quite accessible to the reader familiar with the usual university course of mathematics and with elements of probability theory. The methods described are illustrated by a large number of examples from different fields of practice. The book is intended for a wide range of readers - engineers, economists, researchers and business executives interested in the application of mathematics to the justification of optimal solutions.