From rather modest beginnings, the British Combinatorial Conference grew into an established biennial international gathering. A successful format for the series of conferences was established, whereby several distinguished mathematicians were invited to give a survey lecture and to write a paper for the conference volume. The 1983 conference was held in Southampton, and this volume contains the invited papers, comprising three each from the United Kingdom, continental Europe and the United States. These papers cover a broad range of combinatorial topics, including enumeration, finite geometries, graph theory and permanents. The book will be of value not only to mathematicians, but also to scientists, engineers and others interested in combinatorial ideas.