A conference on Low Dimensional Topology was held at the University College of North Wales, Bangor, on July 2–5, 1979, with 63 participants.

Four principal speakers were invited:

W. Thurston gave four lectures on “Hyperbolic geometry and 3–nanifolds” and one lecture on “The Smith conjecture”.

A. Casson gave one lecture on “Bordisms of automorphisms of surfaces” and two lectures on “Fake S3 × ℝ”.

R.D. Edwards gave three lectures on “The double suspension of homology 3-spheres”.

L. Siebenmann gave two lectures on “Fake S3 × ℝ” and one lecture on “Algebraic knots”.

The articles of this volume were either presented to the conference, or arose out of it. All were refereed.

Of the lectures of the principal speakers, only those of W. Thurston appear here. The notes were written up by Peter Scott, and we asked him to write a brief survey as an introduction.

The four lectures on fake S3 × ℝ correspond to a Séminaire Bourbaki exposé (February 1979, No. 576) by Siebenmann, based on A. Cassonfs work and M. Freedman's article in Annals of Math. 110 (1979) 177–201.

L. Siebenmann's lecture on algebraic knots was an introduction to material in a monograph entitled “New geometric splittings of classical knots” written jointly with F. Bonahon, which will appear shortly in this series, indeed as a second volume of these proceedings.

Peter Stefan's work on Whitehead's conjecture in 1978 has been a stimulus to subsequent research, and we felt his seminal letter of May, 1978, should be published.