Preface. 1. Introduction to Riemannian Manifolds. 2. Canonical Differential Operators Associated to a Riemannian Manifold. 3. Spectral Properties of the Laplace-Beltrami Operator and Applications. 4. Isospectral Closed Riemannian Manifolds. 5. Spectral Properties of the Laplacians for the De Rham Complex. 6. Applications to Geometry and Topology. 7. An Introduction to Witten-Helffer-Sj strand Theory. 8. Open Problems and Comments. Appendix. Subject...