This volume contains the invited talks from the 18th British Combinatorial Conference, held in 2001.This volume contains the proceedings of the 18th British Combinatorial Conference. This meeting, held every two years is now a key event for mathematicians working in combinatorics throughout the world. The papers contained here are from the invited speakers and are thus of a quality fitting for the event. This book will be a valuable reference for researchers in a variety of branches of combinatorics. However, graduate students will find much here that will be of use for future directions in their research.This volume contains the proceedings of the 18th British Combinatorial Conference. This meeting, held every two years is now a key event for mathematicians working in combinatorics throughout the world. The papers contained here are from the invited speakers and are thus of a quality fitting for the event. This book will be a valuable reference for researchers in a variety of branches of combinatorics. However, graduate students will find much here that will be of use for future directions in their research.This volume contains the proceedings of the 18th British Combinatorial Conference. This meeting, held every two years is now a key event for mathematicians working in combinatorics throughout the world. The papers contained here are from the invited speakers and are thus of a quality fitting for the event. This book will be a valuable reference for researchers in a variety of branches of combinatorics. However, graduate students will find much here that will be of use for future directions in their research.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 colourilST