Mike Hitchman's open-content text Geometry with an Introduction to Cosmic Topology approaches geometry through the lens of questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have an edge? Is it infinitely big?
This text develops non-Euclidean geometry and geometry on surfaces at a level appropriate for undergraduate students who have completed a multivariable calculus course and are ready for a course in which to practice habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text is also suited to independent study, with essays and discussions throughout, over 200 exercises, and nearly as many figures. Dynamic geometry activities complement the material as well (follow the Text Extras link above). More about the text can be found in the Preface.
The current edition is the July 2017 Edition.
An updated version is scheduled to be posted March 1, 2018. This update will correct a handful of typos and some indexing errors in the online edition of the text.