This volume is the proceedings of the programme Spaces of Kleinian Groups and Hyperbolic 3-Manifolds held at the Isaac Newton Institute in Cambridge, 21 July–15 August 2003. It is a companion volume to Kleinian Groups and Hyperbolic 3-Manifolds, London Mathematical Society Lecture Notes 299, the proceedings of a conference with the same title held at the Mathematics Institute, University of Warwick, 11–15 September 2001.

The period surrounding these two conferences has seen a series of remarkable advances in our understanding of hyperbolic structures on 3-manifolds. Many of the outstanding issues immediately preceding the Newton Institute meeting related to difficulties in extending results from manifolds with incompressible boundary to the general case. Proofs of Thurston's ending lamination conjecture and the Bers–Sullivan–Thurston density conjecture for general tame groups were announced at the meeting, and the picture was completed not long after the Newton programme, with two independent proofs of Marden's tameness conjecture. As a result, we now have a very clear understanding of the internal geometry of hyperbolic 3-manifolds, combined with an increasingly detailed, but quite intricate, picture of the topology and geometry of the associated deformation spaces of discrete groups.

The Newton Institute meeting turned out to be the international gathering at which many of these new results were disseminated. Almost all the primary contributors took part. Quite how rapid progress has been only became apparent to many of us during the meeting, which will be remembered as a milestone at which all of the new ideas were brought together.