The British Combinatorial Conference is held every two years and is now a key event for mathematicians worldwide, working in combinatorics. This volume is published on the occasion of the 18th meeting, which was held 1st-6th July 2001 at the University of Sussex. The papers contained here are surveys contributed by the invited speakers, and are thus of a quality befitting the event. There is also a tribute to Crispin Nash-Williams, past chairman of the British Combinatorial Committee. The diversity of the subjects covered means that this will be a valuable reference for researchers in combinatorics. However, graduate students will also find much here that could be of use for stimulating future research.