This book is an introduction to the theory and applications of "modern geometry" roughly speaking, geometry that was developed after Euclid. It covers three major areas of non-Euclidean geometry and their applica- tions: spherical geometry (used in navigation and astronomy), projective geometry (used in art), and spacetime geometry (used in the Special The- ory of Relativity). In addition it treats some of the more useful topics from Euclidean geometry, focusing on the use of Euclidean motions, and includes a chapter on conics and the orbits of planets. My aim in writing this book was to...