This volume contains the invited lectures given at the Sixteenth British Combinatorial Conference, held in July 1997 at Queen Mary and Westfield College, University of London. This biennial conference is a well-established international event, with speakers from all over the world. Contained here is a survey of some of the most important work ever in graph theory, with related papers that will be essential background reading to anyone doing research in this field. Also included is an illustration of how recent developments in group theory lead to advances in graph theory, and an exciting new construction of one of the Mathieu groups. Other articles show how to construct a block design, and how to use finite geometries. An account is given of the computational complexity of counting. The book provides a valuable survey of the present state of knowledge in combinatorics. It will be useful to research workers and advanced graduate students, primarily in mathematics but also in computer science, statistics and engineering.