Notation Chapter 1 What Is Enumerative Combinatorics? 1.1 How to Count 1.2 Sets and Multisets 1.3 Permutation Statistics 1.4 The Twelvefold Way Notes References A Note about the Exercises Exercises Solutions to Exercises Chapter 2 Sieve Methods 2.1 Inclusion-Exclusion 2.2 Examples and Special Cases 2.3 Permutations with Restricted Positions 2.4 Ferrers Boards 2.5 V-partitions and Unimodal Sequences 2.6 Involutions 2.7 Determinants Notes References Exercises Solutions to Exercises Chapter 3 Partially Ordered Sets 3.1 Basic Concepts 3.2 New Posets from Old 3.3 Lattices 3.4 Distributive Lattices 315 Chains in Distributive Lattices 3.6 The Incidence Algebra of a Locally Finite Poset 3.7 The MObius Inversion Formula 3.8 Techniques for Computing MObius Functions 3.9 Lattices and Their MObius Algebras 3.10 The MObius Function of a Semimodular Lattice 3.11 Zeta Polynomials 3.12 Rank-selection 3.13 R-labelings 3.14 Eulerian Posets 3.15 Binomial Posets and Generating Functions 3.16 An Application to Permutation Enumeration Notes References Exercises Solutions to Exercises Chapter 4 Rational Generating Functions 4.1 Rational Power Series in One Variable 4.2 Further Ramifications 4.3 Polynomials 4.4 Quasi-polynomials 4.5 P-partitions 4.6 Linear Homogeneous Diophantine Equations 4.7 The Transfer-matrix Method Notes References Exercises Solutions to Exercises Appendix Graph Theory Terminology Index Supplementary Problems Errata and Addenda