- R. Carter, G. Segal and I.MacDonald: Lectures on Lie Groups and Lie Algebras. London Math. Society Student Texts 32. The lectures by Segal are a beautiful overview of the fundamental ideas of Lie groups and algebras, with geometry and examples emphasized.
- W. Fulton and J. Harris: Representation Theory. Springer GTM 129. The canonical reference for representations, especially for the (Lie) algebraic point of view and basic algebro--geometric aspects.

- G. Mackey: Harmonic Analysis as the Exploitation of Symmetry. Bull. Amer. Math. Soc. 3/1 (1980) 543-699. Reprinted in: The Scope and History of Commutative and Noncommutative Harmonic Analysis. History of Math Vol.5, Amer. Math Soc./London Math Soc. 1992. My favorite (and first) introduction to representation theory, emphasizing its history and origins in probability, number theory and physics. The reprint appears in a volume devoted to Mackey's wonderful representation theory survey articles.
- Other Mackey surveys (besides those in the book above): Unitary Group Representations in physics, probability and number theory (Addison-Wesley 1989) -- a book delving deeper into the ideas of the above survey article.
- W. Schmid: Representations of semi-simple Lie groups. In: Atiyah et al., Representation Theory of Lie Groups. Londom Math Society Lecture Notes 34. Cambridge U. Press 1979. Excellent overview by a master, in a volume full of useful reviews (also Mackey, Bott, Kostant, Kazhdan..)
- W. Schmid: Analytic and Geometric Realization of Representations. In: Tirao and Wallach (eds)., New Developments in Lie Theory and their Applications. Lecture notes overviewing the subject in the title, with a strong emphasis on SL_2.

- K. Vilonen: Representations of SL_2. Course Notes, Northwestern University.
- R. Howe and E.C. Tan: Non-abelian harmonic analysis - applications of SL(2,R). Springer Universitext. A very nice introduction to representations of SL(2,R), with interesting applications to classical analysis.
- V.S. Varadarajan: An Introduction to Harmonic Analysis on Semisimple Lie Groups. Cambridge Studies in advanced math 16. Nice textbook, with an emphasis on SL_2 and good introductions to various topics.
- S. Lang: SL(2,R). Springer GTM. Fairly analytical introduction, alas not very coherent -- read the review by Robert Langlands.

- D. Ramakrishnan and R. Valenza: Fourier Analysis on Number Fields. Springer GTM 186. Contains an introduction to the Pontrjagin duality theory for locally compact abelian groups, and its applications to number theory (Tate's thesis).
- J. Arthur: Harmonic Analysis and Group Representations. Notices of the AMS. Gorgeous introduction to the ideas of Harish-Chandra. Available off AMS website.
- I. Gelfand, M. Graev and I. Piatetskii-Shapiro: Representation Theory and Automorphic Functions. Academic Press. A classic thorough study of representations of SL2 over real, p-adic and adelic fields.
- D. Bump: Automorphic Forms and Representations. Cambridge Studs. Advanced Math. 55. A good and detailed introduction to Langlands program ideas focussed on representations of GL2.
- T. Bailey and A. Knapp (eds): Representation Theory and Automorphic Forms. Proc. Symp. Pure Math 61. Proceedings of an instructional conference, with a variety of great introductory articles. (In particular Schmid, Knapp and Langlands).
- J. Bernstein and S. Gelbart (eds): An Introduction to the Langlands Program. Birkhauser. A very timely collection of introductions to the basic constituents of the Langlands program.
- A. Borel and W. Casselman (eds): Automorphic Forms, Representations and L-functions (the Corvallis volumes). The standard source of information about the Langlands program. Available off the AMS website (see e.g. Arinkin's webpage, below).
- J. Bernstein, Courses on Eisenstein Series and Representations of p-adic Groups. Beautiful expositions. Available at Dima Arinkin's Langlands page.
- Wee Teck Gan, Automorphic Forms and Automorphic Representations: slides for a series of five lectures given in Hangzhou, China giving an excellent overview of the basic theory (available on his web page).