  I give my view of the early history of the discovery of hyperbolic structures
on knot complements from my early work on representations of knot groups into
matrix groups to my meeting with William Thurston in 1976. (This article was
written by Robert Riley about ten years before his death in 2000 and never
submitted for publication. An explanation of why it is being published now and
some information about Riley and this article is given in the article by Brin,
Jones and Singerman which accompanies this article in this issue of the
[journal | arxiv].)
