Lectures on the theory of functions of a complex variable are designed for a reader familiar with the main course of mathematical analysis in the volume, for example, a textbook, part P, V.A. Ilyin, E.G. Poznyak. This course consists of 18 lectures. Fundamental concepts such as continuity, differentiability and integrability of functions of a complex variable are considered. The issues of the theory of analytic and harmonic functions are studied and the application of this theory to conformal maps.