The reader may distinguish three principal themes in this volume. There is the direct development of homological methods, interlocking neatly with the Euler characteristic theory on one side, and finiteness questions on the other. There is the theory of groups acting on trees, including that of amalgamated free products and HNN groups, and also the Stallings structure theorem. Finally, but at present still in a rudimentary state, there is the technique of relation modules.

In contrast there is a need for examples, general enough to test ideas, but explicit enough to make detailed calculations. Much the most interesting at present are arithmetic and related groups; the study of these was an auxiliary theme.

Thanks are due to the LMS for backing the conference, to the SRC for money to run it, to David Johnson for much work on the organisation, to the staff at Grey College for providing an agreeable background and, of course, to the participants for their contributions.