The Twentieth British Combinatorial Conference was organised jointly by the University of Durham and the Open University. It was held at Durham in July 2005. The British Combinatorial Committee had invited nine distinguished combinatorial mathematicians to give survey lectures in areas of their expertise, and this volume contains the survey articles on which these lectures were based.

In compiling this volume I am indebted to the authors for preparing their articles so accurately and in such a timely manner, and to the referees for their prompt replies and their attention to detail while commenting on the articles. I would also like to thank Roger Astley at Cambridge University Press, and Mike Grannell at the Open University for their advice and help. Finally, without the previous efforts of editors of earlier Surveys, my job would have infinitely more difficult!

The British Combinatorial Committee gratefully acknowledges the financial support provided by the London Mathematical Society, the Institute of Combinatorics and its Applications, and from the EPSRC.