Chapter 1: Ways to choose
1. The essentials of counting
2. Occupancy
3. More on counting
Historical notes
Chapter 2: Generating functions
1. The formal power series
2. The combinatorial meaning of convolution
3. Generating functions for Stirling numbers
4. Bell polynomials
5. Recurrence relations
6. Labelled spanning trees
7. Partitions of an integer
8. Diophantine systems
Historical note
Chapter 3: Classical inversion
1. Inversion in the vector space of polynomials
2. Taylor expansions
3. Formal Laurent series
4.Multivariate Laurent series
5. The ordinary generating function
6. Gaussian polynomials
Notes
Chapter 4: Graphs
1. Cycles, trails and complete subgraphs
2. Strongly regular graphs
3. Spectra, walks, and oriented cycles
4. Graphs with extreme spectra
Notes
Chapter 5: Flows in neworks
1. Extremal points of convex polyhedra
2. Matching and marriage problems
3. The arc coloring lemmas
4. Flows and cuts
5. Related results
6. The "out of kilter" method
7. Matroids and the greedy algorithm
Notes
Chapter 6: Counting in the presence of a group
1. The general theory
2. Recipe for Polya's theorem
3. Examples following the recipe
4. The cycle index
5. More theory
6. Recipe for DeBruijn's result
7. Examples
Notes
Chapter 7: Block designs
1. The basic structure of t-designs
2.Constructions of t-designs
3. Fisher's inequality
4. Extending symmetric designs
5. On the existence of symmetric designs
6. Automorphisms of designs
7. Association schemes
Notes
Chapter 8: Statistical designs
1. Random variables
2. Factorial experiments
3. Introducing the model
4. Blocking
5. Mixed factorials
Notes
Chapter 9: Mobius inversion
1. The Mobius function
2. Mobius inversion on specially ordered sets
3. Results of Weisner and Hall
4. Counting with the Mobius function
5. Surjective morphisms
Notes
Appendices
1. Finite groups
2. Galois fields, vector spaces and finite geometries
3. The four squares theorem and Witt's cancellation law
Hints and solutions to exercises