1. Introduction to algebraic graph theory; Part I. Linear Algebra in Graphic Thoery: 2. The spectrum of a graph; 3. Regular graphs and line graphs; 4. Cycles and cuts; 5. Spanning trees and associated structures; 6. The tree-number; 7. Determinant expansions; 8. Vertex-partitions and the spectrum; Part II. Colouring Problems: 9. The chromatic polynomial; 10. Subgraph expansions; 11. The multiplicative expansion; 12. The induced subgraph expansion; 13. The Tutte polynomial; 14. Chromatic polynomials and spanning trees; Part III. Symmetry and Regularity: 15. Automorphisms of graphs; 16. Vertex-transitive graphs; 17. Symmetric graphs; 18. Symmetric graphs of degree three; 19. The covering graph construction; 20. Distance-transitive graphs; 21. Feasibility of intersection arrays; 22. Imprimitivity; 23. Minimal regular graphs with given girth; References; Index.