Spectral geometry

I wrote these lectures using the material in set of notes "Analysis on manifolds via the Laplacian" available at http: //www .math.harvard. edu/similar to canzani/docs/Laplacian.pdf. The material there corresponds to a year long course, so it contains more topics and many more details. The following references were important sources for these notes: Eigenvalues in Riemannian geometry. By I. Chavel. Old and new aspects in Spectral Geometry. By M. Craiveanu, M. Puta and T. Rassias. The Laplacian on a Riemannian manifold. By S. Rosenberg. Local and global analysis of eigenfunctions on Riemannian manifolds. By S. Zelditch. Enjoy!!