TITLE: What is the best reference for Spectral theory?
QUESTION [11 upvotes]: I'm studying  Bernard Aupetit: A Primer on Spectral Theory
but the textbook we are using is a little bit heavy going for me. Is there a best book to learn about these things?
Thank you.

REPLY [6 votes]: As nobody has mentioned Reed and Simon yet, I will do so:

Reed, Michael and Simon, Barry.  Methods of Modern Mathematical Physics, Academic Press, 1980.

Of course "spectral theory" means different things to different people, depending on what they plan on doing with it.  As the title suggests, Reed and Simon is in principle aimed at mathematical physicists (quantum mechanics, etc) but it is an honest mathematics textbook (all theorems are proved, etc).  The first volume begins with the basics of functional analysis and ends with the spectral theorem, and volumes 2-4 proceed from there.  I think it's a good treatment for any "working analyst"; it's well motivated and down to earth.  Applications to topics such as PDE are made more explicit than in texts such as Conway.  There are also a ton of really good exercises.
This book is a little unusual (in what I think is a good way) in that it includes, and shows the benefits of, Halmos's "multiplication operator" version of the spectral theorem, mentioned already by Jon Bannon.
Unfortunately the current edition is very expensive, so you may want to try to borrow it from a library or colleague at first.