What texts/books are available for progressing into non-commutative harmonic analysis?
I especially like
Lang: SL(2,R) (There is more than just SL(2,R) there)
Folland: A course in abstract harmonic analysis (especially for quasi invariant measures on homogeneous spaces)
Deitmar-Echterhoff: Principles of Harmonic Analysis (especially for the Selberg trace formula, structure of locally abelian groups and the measure theory part)
Barut and Raczka: The Theory of group representations and applications (For Mackey's theory of induced representation)
Montgomery, Zippin: Topological Transformation groups (Structure theory of locally compact groups and Hilbert 5th problem)
I like Taylors Noncommutative Harmonic Analysis.
by Anton Deitmar has the noncommutative setting as one of its goals.
(check Gigapedia, you can get it over there).
" Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups " by Gregory S. Chirikjian and Alexander B. Kyatkin.