Riemannian Geometry - Isaac (City College Chavel - Bog

This corrected and clarified second edition, first published in 2006, includes a new chapter on the Riemannian geometry of surfaces and provides an introduction to the geometry of curved spaces. Its main theme is the effect of the curvature of spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and on those new notions and ideas motivated by curvature itself.