TITLE: Reference on Fourier analysis on compact groups
QUESTION [5 upvotes]: I am looking for a reference for Fourier analysis on compact (Lie) groups. The kind of theorems I would like the book to cover/do are the Peter-Weyl theorem, define Fourier transforms and use the Peter-Weyl theorem to derive the Plancherel theorem.The Peter-Weyl theorem(s?) can be found in multiple references but most of the books I look into do Fourier analyis on locally compact abelian groups.
Any suggestion is welcome, thanks! I am aware of Sepanski's text but I am looking for an alternate text.

REPLY [4 votes]: For a reference which 1) has what you need, 2) is short and elementary (only undergrad point set topology needed, e.g., Ascoli/Arzela Theorem) yet includes detailed proofs, 3) is very clear and pedagogical, 4) is free; I think you will have a hard time finding better than the note "Haar Measure" by Joel Feldman, on his UBC webpage.