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Some useful notes for the beginners:

Prerequisites for the Langlands Program

First Steps with the Langlands Program

A (Very Brief) History of the Trace Formula by James Arthur

Selected Readings on Langlands Program and Related Topics:

1. The work of Robert Langlands:       

http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/

2. The work of Jim Arthur

http://gauss.claymath.org:8888/cw/arthur/index.php

For a comprehensive introduction to the Arthur-Selberg trace formula, see the article by J.Arthur: An introduction to the trace formula (2005)

For another introduction to the Arthur-Selberg trace formula, see

Gelbart, Stephen ,  Lectures on the Arthur-Selberg trace formula . University Lecture Series, 9. American Mathematical Society, Providence, RI, 1996. x+99 pp.

3. Langlands program

Gelbart, Stephen , An elementary introduction to the Langlands program. Bull. Amer. Math. Soc. (N.S.) 10 (1984), no. 2, 177--219.

Knapp, A. W. Introduction to the Langlands program. Representation theory and automorphic forms (Edinburgh, 1996), 245--302 Proc. Sympos. Pure Math., 61, Amer. Math. Soc., Providence, RI, 1997. download

Gelbart, Stephen S. Automorphic forms on adele groups. Annals of Mathematics Studies, No. 83. Princeton University Press, Princeton, N.J.; University of  Tokyo Press, Tokyo, 1975. x+267 pp.

J. Bernstein and S. Gelbart (Editors), An Introduction to the Langlands program

Gelbart, Stephen ; Shahidi, Freydoon Analytic properties of automorphic $L$-functions. Perspectives in Mathematics, 6. Academic Press, Inc., Boston, MA, 1988. viii+131

Stephen S. Gelbart and Stephen D. Miller, Riemann's Zeta Function and Beyond download

4. Langlands and geometric Langlands program

A. Borel and W. Casselman (Editors),  Automorphic Forms, Representations , and L-Functions, Proceedings of Symposium in Pure Mathematics,
Vol. 33, AMS, 1979  http://www.ams.org/online_bks/pspum331/ , http://www.ams.org/online_bks/pspum332/

Here are the individual papers of the book, volume I and volume II:

I. Reductive groups. Representations

II. Automorphic Forms and Representations

III. Automorphic Representations and L-functions

IV. Arithmetical Algebraic Geometry and Automorphic L-functions

Algebraic Groups and Discontinuous Subgroups , Editors: Armand Borel and George D. Mostow
Available at http://www.ams.org/online_bks/pspum9/

5. Langlands program and physics

6. Infinite-dimensional Lie algebras

Minoru Wakimoto, Lectures on infinite-dimensional Lie algebras , World Scientific, 2001.               

Victor Kac, Infinite dimensional Lie algebras , Cambridge University Press, 1990.   

Igor Frenkel, James Lepowsky, Arne Meurman, Vertex operator algebras and the Monster,
Pure and Applied Mathematics, Vol. 134, Academic Press, 1988.

7. The theory of vertex operator algebras or chiral algebras   

1) Yi-Zhi Huang, James Lepowsky and Lin Zhang, Logarithmic tensor product theory for
generalized modules for a conformal vertex algebra .Part I: download

2) Yi-Zhi Huang, James Lepowsky and Lin Zhang, A logarithmic generalization of tensor
product theory for modules for a vertex operator algebra , Internat. J. Math. 17 (2006), 975-1012. download

3) Yi-Zhi Huang, Vertex operator algebras, the Verlinde conjecture, and modular tensor categories,
Proc. Natl. Acad. Sci. USA 102 (2005), 5352--5356.http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=556239

4) James Lepowsky, From the representation theory of vertex operator algebras to modular tensor
categories in conformal field theory , Proc. Natl. Acad. Sci. USA 102(2005), 5304--5305. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=556255

5) Edward Frenkel and David Ben-Zvi, Vertex algebras and algebraic curves, Mathematical
Surveys and Monographs, Vol. 88, American Mathematical Society, 2001.

6) Alexander Beilinson and Vladimir Drinfeld, Chiral algebras, Colloquium Publications, Vol. 51, AMS, 2000.
Preliminary version: http://www.math.uchicago.edu/~arinkin/langlands/chiral/

7) Yi-Zhi Huang, Two-dimensional conformal geometry and vertex operator algebras,
Progress in Mathematics, Vol. 148, Birkhauser, 1997.

8) Yi-Zhi Huang and James, Lepowsky, On the D-module and formal variable approaches to vertex algebras,
in: Topics in Geometry: In Memory of Joseph D'Atri, ed.

9) S. Gindikin, Progress in Nonlinear Differential Equations , Vol. 20, Birkhaser, 1996, 175--202. q-alg/9603020.

10) Igor B. Frenkel, Yi-Zhi Huang and James Lepowsky, On axiomatic approaches to vertex operator
algebras and modules , Mem. AMS, vol. 104, no. 494, 1993.

11) Igor Frenkel, James Lepowsky and Arne Meurman, Vertex operator algebras and the Monster,
Pure and Applied Mathematics, Vol. 134, Academic Press, 1988.

12) Yi-Zhi Huang, Review of Vertex Algebras and Algebraic Curves by E. Frenkel and D. Ben-Zvi ,
Bull. Amer. Math. Soc. * 39 *(2002), 585-591. http://www.ams.org/journal-getitem?pii=S0273-0979-02-00955-2
(This book review contains a brief nontechnical survey of the geometry of vertex operator algebras and conformal field theories.)

13) Yi-Zhi Huang, Riemann surfaces with boundaries and the theory of vertex operator algebras, in: /Vertex Operator Algebras
in Mathematics and Physics/, ed. S. Berman, Y. Billig, Y.-Z. Huang and J. Lepowsky, Fields Institute Communications,
Vol. 39, Amer. Math. Soc., Providence, 2003, 109--125. math.QA/0212308. download

Selection recommended by Dipendra Prasad:

Langlands program needs background in the theory of Algebraic groups, their representations, as well as Algebraic Number Theory and modular forms. Below are certain standard text and articles on these topics. For a beginner, this smaller list might already be quite daunting. Perhaps, then one could read the expository articles mentioned below of Knapp, Gelbart and Arthur, and then learn the relevant material in greater detail from the below mentioned books according to one's fancy.

General exposition to Langlands program:
A.W. Knapp: Introduction to Langlands program, Proceedings of Symposia in Pure Mathematics, vol. 61 (1997), pages 245-302.
S. Gelbart: An Elementary Introduction to Langlands Program, Bulletin of the AMS (1984) 177-219.
J. Arthur: Automorphic Representations and Number Theory, CMS Conference Proceeding, vol. 1, AMS (1981), pages 3-51.

For Algebraic Groups, here are some books:
T.A. Springer: Linear Algebraic Groups, Progress in Mathematics, vol. 9, Birkhauser.
A. Borel: Linear Algebraic Groups, Graduate Text in Mathematics, Springer Verlag.

For Automorphic Forms which is the central concern of the Langlands program, here is the recommended book:
D. Bump: Automorphic Forms and Representations, Cambridge University Press, Cambridge.

For classical theory of modular forms, and the connection to elliptic curves:
N. Koblitz: Introduction to Elliptic curves and modular forms, Graduate Text in Mathematics, vol. 97, Springer Verlag.

For Number Theory:
J. Neukirch: Algebraic Number Theory, Springer Verlag 1999.
J. Frohlich and M. Taylor: Algebraic Number Theory, Cambridge studies in Advanced Math, vol. 27, Cambridge University Press (1993).

For articles at higher level of sophistication, there is a large collection of them in,
Proceedings Symposia in Pure Mathematics of the AMS, vol. 33, edited by Borel and Casselman.
some are quite readable too, and many are essential reading even now, such as the article of A. Borel on "Automorphic L-functions."

Seletion recommended by Solomon Friedberg:

Connections between L-functions, multiple Dirichlet series, and analytic number theory:

G. Chinta, S. Friedberg, J. Hoffstein, Multiple Dirichlet series and automorphic forms, Proc. Symp. Pure Math. 75 (2006), 3--41. download

B. Brubaker, D. Bump, G. Chinta, S. Friedberg, J. Hoffstein, Weyl group multiple Dirichlet series I, Proc. Symp. Pure Math. 75 (2006), 91--114. download

B. Brubaker, S. Friedberg, D. Bump, Weyl group multiple Dirichlet series II: the stable case, Inventiones Math 165 (2006), 325--355. For a .pdf file, click here. For an older .pdf version of the paper that contains a more coordinatized treatment, click here.

B. Brubaker, D. Bump, S. Friedberg, J. Hoffstein, Weyl group multiple Dirichlet series III: Eisenstein series and twisted unstable A_r, to appear in Annals of Mathematics.download

G. Chinta, S. Friedberg, J. Hoffstein, Asypmtotics for sums of twisted L-functions and applications, in: Automorphic Representations, L-functions and Applications: Progress and Prospects, Ohio State University Mathematical Research Institute Publications 11, de Gruyter, 2005, pp. 75--94.

B. Brubaker, S. Friedberg, J. Hoffstein, Cubic twists of GL(2) automorphic L-functions, Inventiones Math. 160 (2005), 31--58.download

Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory, edited by S. Friedberg (Managing Editor), D. Bump, D. Goldfeld, J. Hoffstein, Proceedings of Symposia in Pure Mathematics, Volume 75, American Mathematical Society (Providence, RI), 2006.

Bump, Daniel The Rankin-Selberg method: an introduction and survey. Automorphic representations, $L$-functions and applications: progress and prospects, 41--73, Ohio State Univ. Math. Res. Inst. Publ., 11, de Gruyter, Berlin, 2005.

Shahidi, Freydoon, Automorphic $L$-functions and functoriality. Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 655--666, Higher Ed. Press, Beijing, 2002. 11F70 (11R39 11S37)

Shahidi, Freydoon, Functoriality and small eigenvalues of Laplacian on Riemann surfaces. Surveys in differential geometry. Vol. IX, 385--400, Surv. Differ. Geom., IX, Int. Press, Somerville, MA, 2004. 11F72 (11F70 11R39 11R42)

Arthur, James(3-TRNT), The principle of functoriality. Mathematical challenges of the 21st century (Los Angeles, CA, 2000).Bull. Amer. Math. Soc. (N.S.) 40 (2003), no. 1, 39--53 (electronic)

F.Shahid, Automorphic $L$-functions: a survey. Automorphic forms, Shimura varieties, and $L$-functions, Vol. I (Ann Arbor, MI, 1988), 415--437, Perspect. Math., 10, Academic Press, Boston, MA, 1990. [This article is necessarily out-of-date, but may still be useful as an introduction.]

Cogdell, James W.; Kim, Henry H.; Murty, M.Ram, Lectures on automorphic $L$-functions. Fields Institute Monographs 20. (2004)

Goldfeld, Dorian, Automorphic Forms and L-Functions for the Group GL(n,R),  Series: Cambridge Studies in Advanced Mathematics (No. 99)
http://www.cambridge.org/us/catalogue/catalogue.asp?isbn=0521837715

Iwaniec, Henryk; Kowalski, Emmanuel, Analytic number theory. American Mathematical Society Colloquium Publications, 53. American Mathematical Society, Providence, RI, 2004. xii+615 pp. ISBN: 0-8218-3633-1

Iwaniec, Henryk, Spectral methods of automorphic forms. Second edition. Graduate Studies in Mathematics, 53. American Mathematical Society, Providence, RI; Revista Matemathica Iberoamericana, Madrid, 2002. xii+220 pp. ISBN: 0-8218-3160-7

Moreno, Carlos Julio, Advanced analytic number theory: $L$-functions. Mathematical Surveys and Monographs, 115. American Mathematical Society, Providence, RI, 2005. xx+291 pp. ISBN: 0-8218-3641-2.

An introduction to the Langlands program. Lectures presented at the Hebrew University of Jerusalem, Jerusalem, March 12--16, 2001. Edited by Joseph Bernstein and Stephen Gelbart. Birkhauser Boston, Inc., Boston, MA, 2003. x+281 pp. ISBN: 0-8176-3211-5.

Automorphic representations, $L$-functions and applications: progress and prospects. Proceedings of a conference honoring Steve Rallis on the occasion of his 60th birthday held at Ohio State University, Columbus, OH, March 27--30, 2003. Edited by James W. Cogdell, Dihua Jiang, Stephen S. Kudla, David Soudry and Robert Stanton. Ohio State University Mathematical Research Institute Publications, 11. Walter de Gruyter & Co., Berlin, 2005.

Erez Lapid's lecture notes:

More publications on Langlands program:

James Arthur, The principle of functoriality. Mathematical  challenges of the 21st century (Los Angeles, CA, 2000). Bull. Amer.  Math. Soc. (N.S.) 40 (2003), no. 1, 39--53 available electronically at http://www.ams.org/journal-getitem?pii=S0273-0979-02-00963-1

On the Corvallis-Proceedings: A. Borel and W. Casselman (Editors), Automorphic Forms, Representations, and L-Functions, Proceedings of Symposium in Pure Mathematics, Vol.  33, AMS, 1979.

The Corvallis-Proceedings is surely excellent and I wouldn't miss it, but in many parts it is also obsolete by now. There are more recent accounts, like the Ann Arbor Proceedings (which officially was the successor of the Corvallis-meeting) or the Edinburgh conference proceedings:

Representation theory and automorphic forms. Papers from the Instructional Conference held in Edinburgh, March 17--29, 1996. Edited by T. N. Bailey and A. W. Knapp. Proceedings of Symposia in Pure Mathematics, 61. American Mathematical Society, Providence, RI; International Centre for Mathematical Sciences (ICMS), Edinburgh, 1997. viii+479 pp. ISBN: 0-8218-0609-2

Knapp, Anthony W, Representation theory of semisimple  groups. An overview based on examples. Reprint of the 1986 original. Princeton Landmarks in Mathematics. Princeton University Press,  Princeton, NJ, 2001. xx+773 pp. ISBN: 0-691-09089-0  

The articles of Cartier, Arthur, Borel in the Corvallis proceedings

Continue with the Edinburgh proceedings.            

 

 

 

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