An international conference ‘Groups - St. Andrews 1981’ was held in the Mathematical Institute, University of St. Andrews during the period 25th July to 8th August 1981. The main topics of the conference: combinatorial group theory; infinite groups; general groups, finite or infinite; computational group theory are all well-represented in the survey and research articles that form these Proceedings. Four courses each providing a five-lecture survey, given by Joachim Neubüser, Derek Robinson, Sean Tobin and Jim Wiegold have been expanded, subsequently, into articles forming the first four chapters of the volume. Many of the themes in these chapters recur in the survey and research articles which form the second part of the volume.

Methods and techniques such as homology, geometrical methods and computer implementation of algorithms are used to obtain group theoretical results. Computational methods are surveyed in several articles in particular the major survey by Joachim Neubüser and find application in papers on Burnside groups and finite simple groups. In fact Burnside groups are discussed in two rather different papers, a survey of groups of exponent four by Sean Tobin and a major contribution to the exponent five case by Marshall Hall and Charles Sims. Derek Robinson exploits the way in which cohomology groups arise in group theory to establish some splitting and near-splitting theorems. Rudolf Beyl also uses homological techniques to discuss group extensions.