Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology (GCT) uses Möbius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe.
The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits. GCT is suitable for a semester course in non-Euclidean geometry or as a guide to independent study, with over 200 exercises and several essays on topics including the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe. More about the text can be found in the Preface.
Reading the text
Geometry with an Introduction to Cosmic Topology appears in three formats. It can be read online as a collection of webpages, it can be downloaded as a pdf, and an inexpensive bound copy (6 x 9 paperback, about $11 US) is avialable for purchase here.
Geometry with an Introduction to Cosmic Topology by Michael P. Hitchman is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.