- Basic notions of linear algebra: brief recollection. The language of Hom spaces and the corresponding canonical isomorphisms. Tensor product of vector spaces.
- Group Theory: Isomorphism theorems, group actions, Jordan-Hoelder theorem, Sylow theorems, direct and semidirect products, finitely generated abelian groups, simple groups, symmetric groups, linear groups, nilpotent and solvable groups, generators and relations.
- Ring Theory: Rings, ideals, Euclidean domains, principal ideal domains, and unique factorization domains.
- Modules: Modules and algebras over a ring, tensor products, modules over a principal ideal domain

- Lang,
*Algebra*, 3rd ed. - Dummit and Foote,
*Abstract Algebra*, 2nd ed.

- Paul Selick's course notes (around 2011)
- Dror Bar Natan's course page (2014)
- Rotman, Robinson both in the GTM series (for groups; they cover much more)

- Homework (roughly 5 assignments): 25%
- Term test: 25%
- Final: 50%

The final will be on

- Assignment 1, due Fri Oct 9
- Assignment 2, due Fri Oct 16 (or Oct 19 if you don't need it graded before the term test)
- Assignment 3, due Fri Nov 6
- Assignment 4, due Fri Nov 20
- Assignment 5, due Wed Dec 9 (or Dec 11 if you don't need it graded before the final exam)

- George Bergman's companion to Lang's Algebra
- Handout by Dror Bar Natan on simplicity of A_n (n \ge 5)
- An example of a PID that is not Euclidean. (There is a much nicer proof that this ring is a PID, but it requires some algebraic number theory.)