Basic Counting
Recurrence Relations and Generating Functions
Probabilistic Method
Some Extremal Problems
Linear-Algebraic-Methods
The Pigeon Hole Principle
Ramsey Theory
Partially Ordered Sets
Combinatorial Games
Polya Theory of Counting



Background Material

Graph Theory
Discrete Probability
GeneratingFunctionology by H. Wilf
Notes on Moser-Tardos Algorithm by J. Spencer
Applied Combinatorics by M.T. Keller and W.T. Trotter
Linear algebra methods in combinatorics : with applications to geometry and computer science by Babai and Frankl