This interesting book is the English translation of the first French edition published in 2001 by Jean-Pierre Luminet, an astrophysicist at the Paris-Meudon Observatory in France. The main aim of the book is to describe a particular approach to cosmology. The author discusses the topology of the universe, which is not a simple theme for popularisation. To understand the main topics, there is a requirement for a deeper knowledge of mathematics (e.g. non-Euclidean geometry, the classification of surfaces, the classification of three-dimensional spaces and symmetries), physics (the theory of relativity, the curvature of the universe and cosmic crystallography), astrophysics (astronomical distances, cosmic repulsions, etc.) and the history of cosmological ideas and philosophical concepts of the cosmos and spaces.

The central notion is the theory of “the wraparound universe”. The author discusses a model of wrapped universes, their experimental ramifications, problems of their sophisticated observations and their consequences (e.g. size of space, fraction of distant galaxies, folds in the universe, expansion and the infinite, the rate of expansion and the age of the universe). The author also tries to explain the most important parts of general relativity, big bang models and cosmic topology. The book is very well written and nicely illustrated; the author uses a simple graphical representation to solve and explain complex problems. The author combines his understanding of history, scientific knowledge and expository skill to produce the book, which can be recommended to all readers interested in mathematical and astronomical ideas and cosmology, as well as the topology of the universe.