Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation This mathematical introductory textbook reveals that even the most basic question in celestial mechanics the Kepler problem leads to a cornucopia of geometric concepts conformal & projective transformations spherical & hyperbolic geometry notions of curvature & the topology of geodesic flows For advanced undergraduate & beginning graduate students this book explores the geometric concepts underlying celestial mechanics & is an ideal companion for introductory courses The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry & topology Numerous exercises historical notes & an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics