At the moment I am trying to understand the proof of the Fredholm property in Salamon's notes on Floer homology. There I came across the notion of an unbounded operator on a (real) Hilbert space which is symmetric and does not have $0$ as an eigenvalue. It is then claimed that the operator generates strongly continuous semigroups on the respective eigenspaces.
In fact I would like to understand these notions, but I don't seem to find good introductory texts. Since the topic seems rather old googling mostly gives me very recent result which are in particular much too specific.
Can anyone give me a reference on symmetric unbounded operators on real Hilbert spaces and their corresponding semigroups?