I'm looking for several references on the spectral analysis of the Laplacian operator. It is such a well-known topic, but I'm a bit struggling to locate modern systematic expositions in the literature.

I'd appreciate multiple suggestions that explore the topic using different approaches too.

I'm particularly interested in the variational characterization of the eigenvalues and eigenfunctions.

Eigenvalues in Riemannian Geometry. $\endgroup$ – Nate Eldredge Jun 14 '17 at 14:29