This first volume of a two-volume book contains selected papers from the international conference Groups St Andrews 2009. Leading researchers in their respective areas, including Gerhard Hiss and Volodymyr Nekrashevych, survey the latest developments in algebra.

Groups St Andrews 2009 was held in the University of Bath in August 2009 and this first volume of a two-volume book contains selected papers from the international conference. Five main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the proceedings. This volume contains the contributions by Gerhard Hiss (RWTH Aachen) and Volodymyr Nekrashevych (Texas A&M). Apart from the main speakers, refereed survey and research articles were contributed by other conference participants. Arranged in alphabetical order, these articles cover a wide spectrum of modern group theory. The regular proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past 30 years. Earlier volumes have had a major impact on the development of group theory and it is anticipated that this volume will be equally important.