Combinatorial methods of discrete mathematics are now both very general principles and specific ways of solving a wide range of problems of discrete mathematics. This monograph focuses on enumeration tasks related to the calculation of the number of combinatorial configurations. The presence of sufficiently general principles for solving such problems, in particular, is provided by the general combinatorial scheme built by the author - a unified system of approach to the formulation and solution of these problems. At the same time, specific ways of solving them are usually based on the use of the apparatus of producing functions, the systematic presentation of which makes up most of the contents of the book.