Lecture 1: Introduction to algebraic structures via universal algebra
Lecture 2: Monoid-oids (aka Categories), some general remarks about groups
Lecture 3: The orbit-stabilizer theorem and the class equation
Lecture 6: Putting groups back together -- group extensions
Lecture 7: An accounting of structures, Nilpotent groups, part 1
Lecture 8: Free groups, part 1
Lecture 9: Free groups, part 2: universal properties and adjunctions
Lecture 10: Nilpotent groups, part 2; Solvable groups
Lecture 11: Rings: definitions and examples
Lecture 12: Basic properties of rings and ideals; fractions and localization, part 1
Lecture 13: Fractions and localization, part 1; Chinese remainder theorem; Principal ideal domains
Lecture 14: Unique factorization domains and Gauss' Lemma
Lecture 15: The Hilbert basis theorem; Introduction to modules
Lecture 16: More modules; tensor products, part 1
Lecture 17: Tensor products, part 2
Lecture 18: Tensor products, part 3; bilinear forms; intro to vector spaces
Lecture 19: Vector space notions: duals, matrices, Kroneker products, tensor algebras
Lecture 20: Symmetric and Exterior algebras. Start of modules over a PID
Lecture 21: The structure of modules over a PID
Lecture 22: Examples and application of the structure theory for modules over a PID
Lecture 23: Jordan-Holder for X-groups. Setting the stage for the Yoneda Lemma
Lecture 24: Some categorical notions and the Yoneda Lemma. Introduction to representations of finite groups.
Lecture 25: Representations of finite groups, part 2.
Lecture 26: Representations of finite groups, part 3; Burnside's Theorem.