The main objective is to understand the representation theory of finite groups: basic structure and important example.

After some basic preliminaries, we will loosely follow Etingof et. al.'s book, chapters 3-5
The book can be found online:
https://math.mit.edu/~etingof/reprbook.pdf

Wikipedia: "Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication)."
Motivation for the initial development of representation theory came from physics, where especially in quantum mechanics, representations of the group of symmetries of a physical system contain physical information about that system (like possible energy levels, ex: https://physics.stackexchange.com/questions/500861/eigenspaces-of-the-hydrogen-atom-as-representations-of-so3)
Nowadays, representation theory is known to have applications in physics, chemistry and other sciences.
In mathematics many important current developments are related to representation theory, like the Langlands program studies automorphic forms and representations (these are the 4th level in Harish-Chandra's philosophy of cups forms; we will study the first level, the symmetric group and the second level in low rank: GL_2(F_q)) and their relations to number theory and geometry, while there is currently a lot of interest in the representation theory of algebraic groups in characteristic p as well as quantum groups and Hecke algebras. This class should be considered as an introduction to the basics of the theory that can then be used to study more complicated topics.

Abstract Algebra MAT301 (302 is also good, but not required)
Linear Algebra (at the level of MAT 400, in particular one should be familiar with proofs in Linear algebra, vector spaces over general fields, tensor products, symmetric and alternating powers etc. )
If you are interested in taking the class, but haven't taken MAT400, look at Manin's book https://www.math.mcgill.ca/darmon/courses/19-20/algebra2/manin.pdf and see if you are comfortable with
Chapter I sections 1-7 and Chapter 4, sections 1,2,3,5,6.
Otherwise, feel free to contact me to ask for advice.

midterm 35%
final 35%
homework 30%
If you miss the classes more than or equal to 6 times it is automatically Fail (F)

Etingof's book will the main reference. Other references are
Serre's book: Linear representations of Finite groups
Sophie Morel's lecture notes: https://morel.perso.math.cnrs.fr/rep_theory_notes.pdf
https://people.math.harvard.edu/~landesman/assets/representation-theory.pdf
https://users.metu.edu.tr/sozkap/513-2013/Steinberg.pdf

Will be updated in the future

in person lecture.