Basic Counting
Recurrence Relations and Generating Functions
Probabilistic Method
Some Extremal Problems
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