This second edition of Analytic pro-p groups has been prepared by two of the authors, Marcus du Sautoy and Dan Segal. We thank Avinoam Mann for contributing Appendix A, and both him and John Dixon for giving us a free hand.

Apart from minor changes in wording and presentation, the book differs from the first edition in the following respects.

• Most of the content of the original Chapter 6 has been redistributed among the other chapters and the ‘Interludes’; as a result, the new Chapter n takes the place of the old Chapter n + 1 for n = 6, 7,8 and 9.

• Chapters 10–13 are new, as are §§5.4, 6.5, 6.6, 7.4 and Interludes A, B, D and E (Interlude B is based on material from the old §§6.1 and 6.2).

• Some of the old exercises have been incorporated into the main text; many new exercises have been added.

• The following sections have undergone major revision: §§3.3, 4.4, 4.5, 7.1, 7.2, 8.1, 9.4 and 9.5.

• The old §6.6 has been left out, as has most of the old §6.2.

• The bibliography has been updated and expanded.

We wish to thank several readers, and especially one reviewer, of the first edition, who pointed out a number of errors – typographical and mathematical. We are grateful to the American Mathematical Society for permission to reproduce Interlude C, which first appeared in the Bulletin of the American Mathematical Society.