TITLE: Harmonic analysis on semisimple groups - modern treatment
QUESTION [19 upvotes]: For my finals, I am digging through the book by Varadarajan An introduction to harmonic analysis on semisimple Lie groups. I find it a rather hard read and I feel it's a bit outdated now. Any recommendation of a more modern (and/or) introductory treatment to the topics covered by this book would be greatly appreciated.
I am more interested in the representation theory, although I find the connection to harmonic analysis intriguing. Having learned finite-dimensional representation theory I wanted to move on to the infinite-dimensional one. From harmonic analysis I know only the classical Pontryagin duality, which I thought is enough to get me started, but I've found Varadarajan's approach based on examples difficult to follow.

REPLY [7 votes]: The first thing one should keep in mind is that harmonic analysis on semisimple Lie groups is very different from the "abstract harmonic analysis" a la Loomis or Hewitt and Ross dealing with locally compact abelian groups. The semisimple case was developed in the large part by Harish-Chandra and his papers (reprinted in his 4 volume Collected papers), while considerably older than Varadarajan's book, are still a good source of results and inspiration for many of us.
For an introduction to the subject, I warmly recommend Howe and Tan's book cited by Jim. It treats from the representation theory point of view the simplest nontrivial case, nonabelian harmonic analysis related to $SL(2,\mathbb{R}).$ The book uses elementary tools, and yet it deals with a wide range of topics. Elements of Harish-Chandra's theory for general reductive Lie groups may be found in Howe's survey article A century of Lie theory. 
The theory of special functions and harmonic analysis on classical symmetric spaces and reductive symmetric spaces based on representation theoretic approach with different flavor is exposed in the books by Vilenkin, Helgasson, and Heckman and Schlichtkrull, which provide good complementary accounts of this theory.