The textbook was created on the basis of lectures given by the authors for several years at the Physics Department of Moscow State University. The book sets out the theory of functions of the complex variable and operational calculus. Examples of application of complex variable function theory methods are given. The basic concepts of the theory of functions of many complex variables are given. The book also gives examples of the application of the methods of the theory of functions of a complex variable to the problems of hydrodynamics and electrostatics, and discusses some issues of the pass method and the Wiener-Hopf method.