We live in a three-dimensional space; what sort of space is it? Can we build it from simple geometric objects? The answers to such questions have been found in the last 30 years, and Outer Circles describes the basic mathematics needed for those answers as well as making clear the grand design of the subject of hyperbolic manifolds as a whole. The purpose of Outer Circles is to provide an account of the contemporary theory, accessible to those with minimal formal background in topology, hyperbolic geometry, and complex analysis. The text explains what is needed, and provides the expertise to use the primary tools to arrive at a thorough understanding of the big picture. This picture is further filled out by numerous exercises and expositions at the ends of the chapters and is complemented by a profusion of high quality illustrations. There is an extensive bibliography for further study.

'… a far-reaching introduction and report on the development and the recent progress in the field of Kleinian groups and their associated hyperbolic-3 manifolds … The book contains a lot of information in a rather condensed form; it is stimulating to read (probably more as a handbook and guide to the main concepts and the relevant literature than systematically in a linear order), and most useful to get an orientation in the field and its literature as well as to learn about the basic concepts and constructions.'

Source: Mathematical Reviews

'… contains a lot of material and can be very valuable for getting an overview of this very broad and important field …'

Source: EMS Newsletter