This volume contains the invited talks from the 18th British Combinatorial Conference, held in 2001.

1. Crispin Nash-Williams J. Sheehan; 2. The Penrose polynomial of graphs and matroids M. Aigner; 3. Cyclic designs I. Anderson; 4. Orthogonal designs and space-time codes for wireless communication A. R. Calderbank and A. F. Naguib; 5. Sampling and counting unlabelled structures L. A. Goldberg; 6. Graphs on surfaces and graph minors B. Mohar; 7. Graph colouring with the probabilistic method M. S. O. Molloy; 8. The interplay between graphs and matroids J. G. Oxley; 9. Ovoids, spreads and m-systems of finite classical polar spaces J. A. Thas; 10. List colourings of graphs D. R. Woodall.