During the academic year 1983/84, the Science and Engineering Research Council of the United Kingdom gave generous financial support for two symposia, at the Universities of Warwick and Durham, on hyperbolic geometry, Kleinian groups and 3-dimensional topology. The symposium at Durham was also sponsored by the London Mathematical Society. I would like to express my thanks to both the SERC and the LMS for their help and support. It is a pleasure to acknowledge the help of my co-organizer at Durham, Peter Scott, who was also an unofficial co-organizer at Warwick. He made an essential contribution to the great success of the symposia.

The world's foremost contributors to this very active area were all invited, and nearly all of them came. The activity centred on the University of Warwick, and climaxed with a 2-week long intensive meeting at the University of Durham during the first 2-weeks of July 1984. There was earlier a period of intense activity during the Easter vacation of 1984, when a number of short introductory lectures were given. The text of the most important of these series of lectures, by S.J. Patterson, is published in these Proceedings.

The papers published here are the result of an invitation to all those attending the two Symposia to submit papers. Not all the papers submitted were the subject of talks given during the Symposia – the contents of the Proceedings are based on their relevance to the subject, and not on their accuracy as documents recording the events of the Symposia.