In the Anglo-American system of university education, the first half of the textbook is for an undergraduate course in elementary differential geometry, and the second half for a beginning course in Riemannian geometry. The topics are notations and prerequisites from analysis, curves in Rn, the local theory of surfaces, the intrinsic geometry of surfaces, Riemannian manifolds, spaces of constant curvature, and Einstein spaces. This third English edition incorporates changes in all six German editions, the most recent published in 2013. Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com)