This book contains the proceedings of a conference on group theory and its applications held in Birmingham, July 10th–13th, 1995, to mark the tenth anniversary of the publication of the ‘atlas of finite groups’. The theme of the conference was to survey developments in the subject during the intervening ten years, and in particular those that were facilitated or inspired in some way by the atlas itself. The conference was supported by a grant from the Engineering and Physical Sciences Research Council, and underwritten by the London Mathematical Society.

The conference brought together all five authors of the atlas, for the first time in many years (if not the first time ever), and a number of distinguished speakers whose talks are listed below. The twenty papers in this volume mostly represent expanded versions of some of these talks. We were also able to celebrate not only the birthday of the atlas of Finite Groups, but the birth of a new atlas, the ‘atlas of Brauer characters’, whose publication was brought forward to enable the first 30 copies to be sold at the conference. If this is volume 2 of the atlas series, perhaps we can expect volume 3 in another ten years.

Although the articles in this book do not fall easily into well-defined categories, we can roughly divide them into those concerned with presentations of groups, those dealing with representations and characters, followed by computational methods, and various aspects of subgroups and geometries, and finally applications and generation.