By Isaac Chavel

This publication presents an creation to Riemannian geometry, the geometry of curved areas, to be used in a graduate path. Requiring merely an figuring out of differentiable manifolds, the writer covers the introductory principles of Riemannian geometry through a variety of extra really good issues. additionally featured are Notes and routines for every bankruptcy, to enhance and increase the reader's appreciation of the topic. This moment version, first released in 2006, has a clearer therapy of many issues than the 1st variation, with new proofs of a few theorems and a brand new bankruptcy at the Riemannian geometry of surfaces. the most subject matters listed below are the impression of the curvature at the traditional notions of classical Euclidean geometry, and the hot notions and ideas influenced through curvature itself. thoroughly new topics created by way of curvature comprise the classical Rauch comparability theorem and its outcomes in geometry and topology, and the interplay of microscopic habit of the geometry with the macroscopic constitution of the gap.