This second volume of Geometric Group Theory, the Proceedings of the Symposium held at Sussex University in 1991, is dedicated entirely to the essay Asymptotic Invariants of Infinite Groups by Mikhael Gromov. His lecture at the conference is reflected in the introductory section, the later sections were written after the conference at the request of several participants. Mikhael Gromov has again opened up new vistas that geometric group theorists may explore in the years to come.

We have adapted his paper slightly for these proceedings and take all responsibility for any errors introduced by our interference. Once again, we would like to thank all participants of the Symposium who helped to make it such an enjoyable event.