This part is based on our study of Bill Thurston's notes (Thurston, 1979), which consist of mimeographed notes produced by Princeton University Mathematics Department as a result of the course given by Thurston in 1978/79. We shall refer to these notes as Thurston (1979). Thurston plans to expand parts of his notes into a book (Thurston, 1979). There is very little overlap between the projected book and this part, whose basis was the joint M.Sc. dissertation written by two of us and supervised by the third. Thanks are due to Thurston who gave us help and encouragement, and also to Francis Bonahon for additional help.

A useful reference for background information on hyperbolic geometry is Epstein (1983) or Beardon (1983).

Our work should be regarded as exposition of results of Thurston. There is not much genuinely original material. Nevertheless the effort of production has been considerable and we hope that readers will find it helpful. One way to use this part would be to read it at the same time as reading Thurston's notes. Certainly Thurston's notes cover ground we do not cover, even in those areas to which we pay particular attention. There is some overlap between our work and that contained in Lok (1984). Two good expositions of related work of Thurston are Morgan-Bass (1984) and Scott (1983).

(Editors' comments. In the intervening years, [T] has become Thurston (1979). This projected book has materialized as Thurston (1997).)