This volume is the proceedings of a workshop on ‘Number Theory and Polynomials’ held at Bristol University, 3–7 April 2006, with about fifty participants. The workshop was the first in a series of workshops sponsored by the Heilbronn Institute for Mathematical Research. During the meeting, the participants exchanged lectures, had informal discussions, and posed problems in the broad subject area defined by the theme of the workshop. Some of the articles in these proceedings are, in whole or in part, the direct outcome of questions posed and ideas raised during the workshop.

The meeting and the proceedings shared the aim of bringing together number-theorists with varied backgrounds having a common interest in problems concerning polynomials. Many of the overseas participants were supported by the Heilbronn Institute for Mathematical Research. The articles in the proceedings are not intended to be a record of the lectures at the meeting: some of the papers are more extensive than the corresponding talks, some of the talks are not represented by papers, and non-speakers were also invited to submit papers on the theme of the workshop. Expository papers and surveys were encouraged, and many of the submissions are of this form. It is hoped that this collection of papers will form a useful resource for new and old researchers in the field.