Riemannian Geometry and Geometric Analysis

The present textbook is a somewhat expanded version of the material of a three-semester course I gave in Bochum. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds. In the first chapter, we introduce the basic geometric concepts, like dif­ ferentiable manifolds, tangent spaces, vector bundles, vector fields and one­ parameter groups of diffeomorphisms, Lie algebras and groups and in par­ ticular Riemannian metrics. We also derive some elementary result