The book is intended for the initial study of the theory of random processes on a strict mathematical basis. It considers the general provisions of the theory (including measure theory and axiomatics of probability theory) and the most important classes of random processes. A number of issues covered in the book have so far only been outlined in magazine articles. The book is designed for undergraduate and graduate students of universities, as well as for non-mathematical specialists who want to familiarize themselves with the basic mathematical methods of the theory of random processes.