We would like to thank Cambridge University Press for encouraging us to produce this new edition of the Proceedings of Groups St Andrews 1981. At the suggestion of Roger Astley of Cambridge University Press we have asked the four main speakers at the 1981 conference to provide brief addenda to their articles. We are delighted that they have all responded positively to this task. Three of the authors have provided their own new pages. The fourth article on ‘An elementary introduction to coset table methods in computational group theory’ has been prepared by us with our friend and collaborator George Havas after some helpful suggestions from Joachim Neubüser. We have also added a short article looking back at twenty-five years of Groups St Andrews conferences.

Although for the 1981 Proceedings we put all the references into a standard form, we have, twenty-five years later, adopted a more relaxed approach and have kept the refereeing style of the addenda as provided by the authors.

Thanks are also due to our colleague Martyn Quick for his help with the preparation of the additional material.