Enumeration: Elementary counting and identities; recurrences and generating functions; Fibonacci, Stirling, Bell and Catalan numbers, inclusion-exclusion and Möbius inversion; partitions; Ferrers diagrams.

Designs: Block designs; triple systems; projective planes; orthogonal Latin squares; Fisher's inequality; Hadamard matrices; connections to codes.

Set Systems and Ordered Sets: Sperner Theory, normalized matching and LYM inequality; Erdos, Ko, Rado theorem; Dilworth and Greene-Kleitman theorems; order dimension; Lattices - distributive, geometric and modular; specials classes of orders, matroids.

Graph Theory: Connectivity; degree sequences; Eulerian graphs and digraphs and Chinese Postman problem; Hamiltonian properties - Chvatal closure, toughness, sufficiency conditions; Turan's theorem; Matching - Berge-Tutte theorem, Gallai-Edmonds structure, alternating paths, König Theorem, vertex covers; coloring and perfect graphs; special graph classes; planar graphs; digraphs and tournaments - Redei's theorem, Gallai-Roy and Gallai-Milgram theorems; Ramsey theory; networks and optimization and connections to linear programming; minimax theorems.

Knowledge of connections between the various topics is also expected.

There are many survey articles, monographs, texts containing this material. The following are suggested references:

1. The Art of Combinatorics (4 volumes, to appear), by D. B. West
2. Introduction to Graph Theory, by D.B. West
3. Combinatorial Theory, by M. Hall Combinatorial Problems and Exercises, by L. Lovasz
4. Applied Combinatorics, by F.S. Roberts
5. Combinatorics of Finite Sets, by I. Anderson