This PDF
covers the following topics related to Riemannian Geometry : Manifolds, Examples
of manifolds, Submanifolds, Tangent spaces,Tangent map, Tangent bundle, Vector
fields as derivations, Flows of vector fields, Geometric interpretation of the
Lie bracket, Lie groups and Lie algebras, Frobenius’ theorem, Riemannian
metrics, Existence of Riemannian metrics, Length of curves, Connections and
parallel transport, Geodesics, The Hopf-Rinow Theorem, The curvature tensor,
Connections on vector bundles.

**Author(s):** Eckhard Meinrenken, University of Toronto

58**Pages**