This book introduces readers to the language of generating functions, which nowadays, is the main language of enumerative combinatorics. The book starts with definitions, simple properties, and numerous examples of generating functions. It then discusses topics such as formal grammars, generating functions in several variables, partitions and decompositions, and the exclusion-inclusion principle. In the final chapter, the author describes applications to enumeration of trees, plane graphs, and graphs embedded in two-dimensional surfaces.

Throughout the book, the author motivates readers by giving interesting examples rather than general theories. It contains numerous exercises to help students master the material. The only prerequisite is a standard calculus course. The book is an excellent text for a one-semester undergraduate course in combinatorics.

Chapter 1. Formal power series and generating functions. Operations with formal power series. Elementary generating functions
Chapter 2. Generating functions for well-known sequences
Chapter 3. Unambiguous formal grammars. The Lagrange theorem
Chapter 4. Analytic properties of functions represented as power series and their asymptotics of their coefficients
Chapter 5. Generating functions of several variables
Chapter 6. Partitions and decompositions
Chapter 7. Dirichlet generating functions and the inclusion-exclusion principle
Chapter 8. Enumeration of embedded graphs
Final and bibliographical remarks