This volume contains 31 papers presented at the conference “Combinatorics in Cambridge”, held in Cambridge, 4-7 August 2003 on the occasion of the 60th birthday of Béla Bollobás. Therefore the authors were chosen with the aim of representing the many areas of mathematics that Béla Bollobás has influenced. The papers are written by excellent scientists in their research areas. Most of the papers are devoted to recent research in graph theory and its applications and connections to other fields of mathematics. Probability theory is used as a tool and new results are presented in many papers. Research in fields like number theory and convex geometry is also contained in some papers of this proceedings. All the papers have also appeared in the journal Combinatorics, Probability and Computing over the last two years.