Includes bibliographical references (p. 537-568) and indexes.

1. Ch. 1. Fundamental concepts: What is a graph? ;
2. Paths, cycles, and trails ;
3. Vertex degrees and counting ;
4. Directed graphs ;
5. Ch. 2. Trees and distance: Basic properties ;
6. Spanning trees and enumeration ;
7. Optimization and trees ;
8. Ch. 3. Matchings and factors: Matchings and covers ;
9. Algorithms and applications ;
10. Matchings in general graphs ;
11. Ch. 4. Connectivity and paths: Cuts and connectivity ;
12. K-connected graphs ;
13. Network flow problems ;
14. Ch. 5. Coloring of graphs: Vertex colorings and upper bounds ;
15. Structure of k-chromatic graphs ;
16. Enumerative aspects ;
17. Ch. 6. Planar graphs: Embeddings and Euler's formula ;
18. Characterization of Planar graphs ;
19. Parameters of planarity ;
20. Ch. 7. Edges and cycles: Line graphs and edge-coloring ;
21. Hamiltonion cycles ;
22. Planarity, coloring, and cycles ;
23. Ch. 8. Additional topics (optional): Perfect graphs ;
24. Matroids ;
25. Ramsey theory ;
26. More extremeal problems ;
27. Random graphs ;
28. Eigenvalues of graphs.