On Friday, 26 March 1993, Paul Erdős celebrated his 80th birthday. To honour him on this occasion, a conference was held in Trinity College, Cambridge, under the auspices of the Department of Pure Mathematics and Mathematical Statistics of the University of Cambridge. Many of the world's best combinatorialists came to pay tribute to Erdős, the universally acknowledged leader of their field.

The conference was generously supported both by the London Mathematical Society and by the Heilbronn Fund of Trinity College. As at former Cambridge Conferences in honour of Paul Erdős, the day-to-day running of this conference was in the able hands of Gabriella Bollobás, with the untiring assistance of Tristan Denley, Ted Dobson, Tom Gamblin, Chris Jagger, Imre Leader, Alex Scott and Alan Stacey. The conference would not have taken place without their dedicated work.

On the eve of Erdős' birthday, a sumptuous feast was held in his honour in the Hall of Trinity College. The words wherein he was toasted are reproduced in the following pages. This volume of research papers was presented to Paul Erdős by its authors as their own toast, gladly offered with their gratitude respect and warmest wishes.

Sadly, before this book reached its printed form, Paul Erdős died. Whereas it was conceived in joy it appears now tinged with sorrow. We feel his loss tremendously. But it is not appropriate that grief should overshadow this volume.