TITLE: Representation theory of locally compact groups
QUESTION [9 upvotes]: My knowledge about representation theory of locally compact groups is rather scattered. As I got more interested with this subject, I would like to know some good references, where I could learn the basic facts of this theory. So I'm looking for the book (or books, if there is no one souce which can cover the material which I want to learn) which will contain:
1. The result that each irreducible representation of compact group is finite dimensional.
2. The theorem which states that for any locally compact group irreducible representations separate the points.
3. Discussion about how the topology on the set of $Irr G$ (classes of) irreducible representation is defined.
4. The answer to the question: if $G$ is compact then $Irr G$ is discrete and if $G$ is discrete then $Irr G$ is compact.
5. Definition of the Plancherel measure.
6. The theorem which states that for any compact group $G$ we have:
a) every representation of $G$ splits into direct sum of irreducible ones
b) every irreducible representation is contained in left regular representation.
I will be very grateful for any help.

REPLY [2 votes]: Gerald  B. Folland, a course in abstract harmonic analysis, is the best source and contains the answers to your questins.