https://en.wikipedia.org/wiki/Langlands_program
We will study the theory of automorphic forms using representation theory and number theory. I will explain some basic properties of automorphic forms/representations and we will study some examples. The hope is to understand some basic principles appearing in the area of math usually called the Langlands program.
We will introduce modular forms, with examples and explain how one can think about them as automorphic forms on SL_2. Then we will study general topics in automorphic forms including (a subset of)
-Tate's thesis
-Eisenstein series
-automorphic representations and real/p-adic representation theory
-Hecke theory and automorphic L-functions
-Langlands correspondence and Langlands functoriality, trace formula etc.
-L-functions and period integrals etc.

At a very basic level you will need: undergraduate abstract algebra (Math 301-302) and undergraduate complex analysis or equivalent.
It will be very helpful if you took a course in number theory (say Math 304) and helpful if you took courses in representation theory (403 and/or 625).

Bump: Automorphic Forms and Representations
Getz, Hahn: An Introduction to Automorphic Representations
Fleig, Gustafsson, Kleinschmidt, Persson: Eisenstein series and automorphic representations
Goldfeld: Automorphic representations and L-functions for the general linear group Vol1, Vol2
Gelbart: Automorphic Forms on Adele Groups
Langlands: On the Functional Equations Satisfied by Eisenstein Series

TBA