This volume derives from a workshop entitled “Approaches to Numerical Relativity” which was held in the week 16-20th December, 1991, in the Faculty of Mathematical Studies at Southampton University, England. It was held principally because it was thought that the time was opportune to begin a dialogue between theorists in classical general relativity and practitioners in numerical relativity. Numerical relativity - the numerical solution of Einstein's equations by computer - is a young field, being possibly only some fifteen years old, and yet it has already established an impressive track record, despite the relatively small number of people working in the field. Part of this dialogue involved bringing participants up to date with the most recent advances. To this end, international experts in the field were invited to attend and give presentations, including Joan Centrella, Matt Choptiuk, John Miller, Ken-Ichi Oohara, Paul Shellard and Jeff Winicour. In addition, a significant number of European scientists, both theoreticians and practitioners in numerical relativity, were invited, the majority of whom attended. In the event, there were some 35 participants, most of whom gave presentations. This volume is largely comprised of the written versions of these presentations (their length being roughly proportional to the time requested by the authors for their presentations).

In an attempt to highlight the distinctive nature of the workshop, I have divided the contributions into Part A, Theoretical Approaches and Part B, Practical Approaches.