This book presents the foundations and concepts of modern combinatorics in a clear and illustrative manner. Its accessible exposition is aimed at students of mathematics, the natural sciences, computer science, and economics, and allows for an easy, example-driven approach to the methods of combinatorics.

Beginning with the basic problems of combinatorics, the reader is gradually introduced to more advanced topics such as generating functions, recurrence relations and Möbius inversion, as well as graph polynomials and finite automata.

A large number of examples and exercises with solutions facilitate understanding and support consolidation and practical application of the material.

This book is a translation of the original German 4th edition. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book may read stylistically differently from a conventional translation.

Peter Tittmann is a researcher and lecturer at Mittweida University of Applied Sciences.