This is a quite complete textbook on enumerative combinatorics which, as the title indicates, stresses, but is not limited to, bijective proofs for counting.
As a textbook it has the positive feature of defining notions from scratch, with detailed accounts starting from basic counting (set theory, sum and product rules, basic combinatorial objects) to the more advanced counting devices (generating functions, Möbius inversion, Pólya theory, symmetric polynomials.) The book includes some topics which are not commonly found in similar textbooks. Among them there are chapters on counting on graphs, on ranking combinatorial objects, on tableaux and on antisymmetric polynomials. The text is organized as to lead the reader from elementary combinatorics to advanced topics at graduate level. Its encyclopedic character makes it also useful as a reference book. The topics are treated with formal rigor and illustrated with numerous examples. Each chapter is complemented with a wealth of exercises, including an appendix with hints to selected ones.
The last chapter collects a miscellania of topics including the Feller-Chung theorems on lattice paths, the hook-length formula, the Pfaffians for counting matchings or a nice proof of the Kasteleyn-Temperley-Fisher formula for domino tilings of a rectangle.