I am interested in mathematical aspects of eigenvalue perturbation theory, in particular which arises in quantum mechanics. I have some knowledge in measure theory, functional analysis, etc. I am trying to find a nice reference to study them.
So far, I have found some nice references as follows. One book is:
Kato, Perturbation Theory for Linear Operators
and I also found many research papers written by Barry Simon (I think he is one of the leading figure in this area), such as:
Coupling constant analyticity for the anharmonic oscillator
Large orders and summability of eigenvalue perturbation theory: A mathematical overview
FIFTY YEARS OF EIGENVALUE PERTURBATION THEORY
and so on.
However, one problem I recognized is that it is too old! In particular, the typesetting is not in LaTeX and is hard to read. Also, I am not sure that these references are 'introductory', i.e., recommended for beginners who want to enter this field. Could you suggest some modern references for the perturbation theory? (Especially, I am interested in time dependent aspects, in particular the rigorous justification of "Fermi gold rule". I am also interested in the singular perturbation theory.)