I may eventually add comments about each entry, and possibly will reorganize things by topic.

I'd like to make this into open-edit database, but that may be awhile in coming (or some energetic young person should volunteer to help with this), so if there's something you'd like to add, please let me know. Also, if you have suggestions for how the list (or future database) should be better organized, I'd be happy to hear them.

Notes and Papers (organized by author)

• Automorphic representations and number theory, James Arthur, CMS Seminar (1981) 49pp.
• The trace formula and Hecke operators, James Arthur, Selberg volume (1989) 17pp.
• Lectures on automorphic L-functions, James Arthur and Stephen Gelbart (1991) 59pp.
• Harmonic analysis and group representations, James Arthur, Notices AMS (2000) 9pp.
• An introduction to the trace formula, James Arthur, Clay Volume (2005) 263pp.
• Report on the trace formula, James Arthur (2007) 12pp.
• A (very brief) history of the trace formula, James Arthur (2007) 11pp.

• The Jacquet-Langlands correspondence, Ioan Badulescu, TIFR Lectures (2001) 21pp.

• Automorphic forms lecture notes, Ben Brubaker, 181pp.

• Relative aspects of the Langlands program lecture notes, Farrell Brumley (2021)

• On Some Applications of Automorphic Forms to Number Theory, Daniel Bump, Solomon Friedberg and Jeffrey Hoffstein, Bull. AMS (1996) 19pp.
• Notes on representations of GL(r) over a finite field, Daniel Bump, 15pp.
• Orbital integral and the Satake isomorphism, Daniel Bump (2004) 24pp.

• L-functions, Kevin Buzzard, TCC course notes (2008) 87pp.

• The infinite fern and families of quaternionic modular forms, Gaetan Chenevier, Galois trimester course, IHP (2010)

• Analytic theory of L-functions for GL(n), Langlands conjectures for GL(n), and Dual groups and Langlands functoriality, James Cogdell, Jerusalem lectures (2001) 29pp., 18pp., 16pp.
• Converse theorems, functoriality and applications to number theory, James Cogdell and Ilya Piatetski-Shapiro, ICM Proceedings, Beijing (2002) 10pp.
• Converse theorems, functoriality and applications, James Cogdell, Quart. J. (Borel volume, 2002), 27pp.
• L-functions and converse theorems for GL(n), James Cogdell, Park City Lecture Notes (2002) 85pp.
• Lectures on L-functions, converse theorems and functoriality for GL(n), James Cogdell, Fields Institute Lectures (2003) 109pp.
• Lecutres on integral representations of L-functions, James Cogdell, Columbia Workshop (2006) 23pp.

• An elementary introduction to the Langlands program, Stephen Gelbart, Bull. AMS (1984), 43pp.
• Lectures on automorphic L-functions, James Arthur and Stephen Gelbart (1991), 59pp.
• Lectures on the Arthur-Selberg Trace Formula, Steven Gelbart, MSRI Lecture Notes (1995) 98pp.

• The arithmetic of elliptic curves - an update, Benedict Gross, Arab J (2009) 17pp.
• From Laplace to Langlands via representations of orthogonal groups, Benedict Gross and Mark Reeder, Bull. AMS (2006), preprint version 60pp.
  Exposition of local representations, packets and Gross-Prasad conjectures

• An introduction to the stable trace formula, Michael Harris, 40pp.
• Galois representations, automorphic forms, and the Sato-Tate conjecture, Michael Harris, Clay research proceedings (2007), 33pp.
• Arithmetic applications of the Langlands program, Michael Harris, Takagi lecture (2009), 61pp.

• Group representations and harmonic analysis from Euler to Langlands [Part 2] Anthony Knapp, Notices AMS (1996), 6pp. and 13pp.
• Introduction to the Langlands program, Anthony Knapp, PSPM 61 (Edinburgh, 1997) 58pp.
• Theoretical aspects of the trace formula for GL(2), Anthony Knapp, PSPM 61 (Edinburgh, 1997) 51pp.
• Applications of the trace formula, Anthony Knapp and Jonathan Rogawski, PSPM 61 (Edinburgh, 1997) 19pp.
• Prerequisites for the Langlands program, Anthony Knapp, Advanced Lectures in Mathematics (China, 2009) 9pp.
• First steps with the Langlands program, Anthony Knapp, Advanced Lectures in Mathematics (China, 2009) 12pp.

• Introduction to endoscopy, Jean-Pierre Labesse, Snowbird Lectures (2006) 54pp.

• A motivated introduction to the Langlands program, M. Ram Murty, Advances in Number Theory (1993), 30pp.
• Selberg's conjectures and Artin L-functions, M. Ram Murty, Bull. AMS (1994), 14pp.
• Recent Developments in the Langlands program, M. Ram Murty, CR Math Acad Sci Can (2002) 22pp.
• Lectures on symmetric power L-functions, M. Ram Murty, Fields Institute Lecture Notes (2004) 81pp.

• Endocsopic theory of automorphic forms, Ngo Bau Chau, ICM 2010, 28pp.

• An introduction to the local Langlands correspondence, Mark Reeder (2012), 26pp.
• From Laplace to Langlands via representations of orthogonal groups, Benedict Gross and Mark Reeder, Bull. AMS (2006), preprint version 60pp.
  Exposition of local representations, packets and Gross-Prasad conjectures

• Functoriality and the Artin conjecture, Jonathan Rogawski, PSPM 61 (Edinburgh, 1997) 23pp.
• Applications of the trace formula, Anthony Knapp and Jonathan Rogawski, PSPM 61 (Edinburgh, 1997) 19pp.
• The nonabelian reciprocity law for local fields, Jonathan Rogawski, Notices AMS (2000) 7pp.

• Automorphic forms course page, Yiannis Sakellaridis

• Serre's Modularity Conjecture, Michael Schein, Winter School on Galois Theory notes (Luxembourg, 2012) 26pp.
  

• Galois Representations [long version] [short version], Richard Taylor, ICM Lecture (2002), 42pp. and 25pp.
• Reciprocity laws and density theorems, Richard Taylor, Shaw lecture (for a general audience) (2007) 19pp.

• (Classical) Automorphic forms course page, Holger Then (2012)

• Automorphic forms and Langlands program, Yannan Qiu, course notes taken by Robert Rhoades (2008) 136pp.

• An elementary introduction to the local trace formulas of J. Arthur. The case of finite groups, Marie-France Vigneras (1991) 19pp.
• Introduction to the Langlands modulo p correspondence for GL(2,Q_p), Marie-France Vigneras, Princeton lectures (2010) 20pp.

• Introductory lectures on automorphic forms, Nolan Wallach, Luminy Summer School (2001) 84pp.

• Advanced Number Theory, Jared Weinstein course notes (2011)
  Background material for and brief intro to automorphic representations

Classic Collections

• Corvallis Proceedings [Volume 1] [Volume 2]
  The Talmud of automorphic forms

• Arthur Archive
• Bill Casselman's Home Page (the (unpublished) book, various essays, course notes, and classics)
  Classics includes Godement's notes on Jacquet-Langlands and Bernstein's notes on p-adic representations, and Casselman's book is classic too!
• Paul Garrett's Vignettes
• Langlands Digital Archive
• James Milne

Recent Collections

• LMFDB's list of lecture notes (number theory, elliptic curves, modular forms and automorphic forms)

• Arizona Winter School
  Yearly week-long school on topics in arithmetic geometry with notes and videos
• Clay Summer School on Galois Representations (Honolulu, 2009)
  Notes by Brinon and Conrad on p-adic Hodge theory, Kisin and Tilouine on deformation theory, Bellaiche on Iwasawa theory
• Galois Trimester, Institut Henri Ponicare, Jan. 4 - Mar. 27, 2010
  Link appears to be broken
• Hakuba 2006 Proceedings (on GSp(4))
  Notes from both introductory and research talks
• Heegner Points and Rankin L-Series (MSRI Volume 49)
  A mix of introductory and research talks
• Papers and Talks on Random Matrix Theory and L-functions from the 2009 Graduate Workshop on Zeta Functions, L-Functions and their Applications
  Notes by Conrey on random matrices, Murty on Artin L-series, and Gonek on the Riemann zeta function
• Representation theory of real reductive Lie groups (Casselman/Milicic conference), Snowbird, Utah, Jun 4-8, 2006
  Notes by Adams on real groups, Labesse on endoscopy, Miller-Schmid on Rankin-Selberg and Arthur's problems for real groups
• Stanford number theory seminars, listed on Brian Conrad's webpage
  Notes from year-long learning seminars on topics such as modularity lifting and work of Mordell, Darmon and Shimura
• Trieste (ICTP) School on Automorphic Forms on GL(n), 2000 (ICTP Lectures Vol 21)
  Notes by Raghunathan, Venkataramana, Cogdell, Prasad-Raghuram, Harder and Wedhom
• Trieste (ICTP) Summer School on Automorphic forms and Shimura Varieties, 2007 (some lecture notes available)
  Notes by Nair, Henniart, Venkataramana, Prasad, Rajan, Edixhoven, Chaudouard, Yu, Jiang

• Kevin Buzzard's notes in a similar spirit to Paul Garrett's vignettes
• Chao Li, a Harvard grad student with various notes online (e.g., this and this)
• Michael Woodbury (notes from some courses, conferences, etc)