Since its inception at Oxford in 1969 the British Combinatorial Conference has become a regular feature of the international mathematical calendar. This year the seventh conference will be held in Cambridge from 13th to 17th August, under the auspices of the Department of Pure Mathematics and Mathematical Statistics. The participants and the contributors represent a large variety of nationalities and interests.

The principal speakers were drawn from the mathematicians of Britain, Europe and America. They were asked to review the diverse areas of combinatorics in which they are expert. In this way it was hoped to provide a valuable work of reference describing the state of the art of combinatorics. All of the speakers kindly submitted their articles in advance enabling them to be published in this volume and made available in time for the conference.

I am grateful to the contributors for their cooperation which has made my task as an editor an easy one. I am also grateful to the Cambridge University Press, especially Mr David Tranah, for their efficiency and skill. On behalf of the British Combinatorial Committee I would like to thank the British Council, the London Mathematical Society and the Mathematics Faculty of Cambridge University for their financial support.