This little book introduces the reader to the use of generating functions. It is based on lectures given by the author at the College of Mathematics of the Independent University of Moscow. Reading the book does not require too much previous knowledge; a good calculus course is almost only what is needed. The book contains many worked out examples and more than 100 exercises. The first chapter is devoted to formal power series and elementary generating functions. The other chapters deal with some well-known sequences but the book also contains material on generating functions of several variables, formal grammars, Dirichlet generating functions and enumeration of graphs. The author does not develop an extensive theoretical background; he prefers to explain topics chosen by means of interesting examples. Brief comments and bibliographical remarks together with the index are useful. This nice book can be used for work in student seminars as well as a source of nice illustrative examples. It can be recommended for libraries and students.