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Aigner M. A Course in Enumeration 2007
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The text is divided into three parts: Basics, Methods, and Topics. This should enable the reader to understand what combinatorial enumeration is all about, to apply the basic tools to almost any problem he or she may encounter, and to proceed to more advanced methods and some attractive and lively fields of research.
As prerequisites, only the usual courses in linear algebra and calculus and the basic notions of algebra and probability theory are needed. Since graphs are often used to illustrate a particular result, it may also be a good thing to have a text on graph theory at hand.
For terminology and notation not listed in the index the books by R. Diestel, Graph Theory, Springer 2006, and D. B. West, Introduction to Graph Theory, Prentice Hall 1996, are good sources. Given these prerequisites, the book is best suited for a senior undergraduate or first-year graduate course

Aigner M. A Course in Enumeration 2007.pdf14.39 MiB