TITLE: Nodes of eigenfunctions and Courant's nodal domain theorem
QUESTION [5 upvotes]: I am looking for a reference for properties of eigenfunctions of the Laplacian (on the Euclidean plane, and maybe also Laplace-Beltrami on a general manifold):

The discreteness of the set of eigenvalues,
Nodes of eigenfunctions,
Courant's nodal domain theorem,
The Faber-Krahn inequality,

and other related results.
I have tried Methods of Mathematical Physics (Courant, Hilbert) but it contains only some of the above, is quite old and a bit hard to read.

REPLY [4 votes]: Adding a second answer to my own question for everyone's benefit:
In the past month I have been reading Eigenvalues in Riemannian Geometry by Isaac Chavel, and it is a good book for these subjects.