These notes arose from a course of lectures given to final year and postgraduate students at the University of Nottingham, and comprise a substantially revised and extended version of my earlier contribution to this series. As before, the emphasis is on concrete examples of groups exhibited in their natural settings and thus to demonstrate at a modest level some of the pervasive connections between group theory and other branches of mathematics. Such is the current rate of progress (both upwards and outwards) in combinatorial group theory that no attempt at completeness is feasible, though it is hoped to bring the reader to within hailing distance of the frontiers of research in one ot two places.

My thanks are due to a host of colleagues, students and friends whose names, too numerous to mention here, may be found scattered through the ensuing pages. It is a pleasure to acknowledge a special debt of gratitude to Professor Sandy Green for introducing me to research mathematics, to Dr E.F. Robertson for his encouragement and for help in correcting the proofs, and to Dr H.R. Morton for much valuable advice on the final chapter. My thanks also go to Professor I.M. James for keeping a paternal eye on things, to Mrs Anne Towndrow for typing half the manuscript, and to the staff of Cambridge University Press for their speed and skill in setting the text (especially the other half).