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1. Graphs 2. Trees 3. Colourings of graphs and Ramsey's theorem 4. Turán's theorem 5. Systems of distinct representatives 6. Dilworth's theorem and extremal set theory 7. Flows in networks 8. De Bruijn sequences 9. The addressing problem for graphs 10. The principle of inclusion and exclusion: inversion formulae 11. Permanents 12. The van der Waerden conjecture 13. Elementary counting: Stirling numbers 14. Recursions and generated functions 15. Partitions 16. (0,1) matrices 17. Latin squares 18. Hadamard matrices, Reed-Muller codes 19. Designs 20. Codes and designs 21. Strongly regular graphs and partial geometries 22. Orthogonal Latin squares 23. Projective and combinatorial geometries 24. Gaussian numbers and q-analogues 25. Lattices and Möbius inversion 26. Combinatorial designs and projective geometry 27. Difference sets and automorphisms 28. Difference sets and the group ring 29. Codes and symmetric designs 30. Association schemes 31. Algebraic graphs: eigenvalue techniques 32. Graphs: planarity and duality 33. Graphs: colourings and embeddings 34. Trees, electrical networks and squared rectangles 35. Pólya theory of counting 36. Baranyai's theorem Appendices.