- The Conjugation Action
- Normalizers and Centralizers of the Conjugation Action
- The Sylow Theorems
- Applications of Sylow Theorems
- Composition Series and Solvability
- Applications of Jordan Holder
- The Commutator, Derived Series, and Solvability
- P-Groups are Solvable
- The Symmetric Group
- Transpositions, Alternating Group and Conjugacy
- Conjugacy in An
- Products of Groups
- Products of Groups, Domains
- Finite Groups
- Rings, Polynomials and Factoring Polynomials
- Field Extensions and the Fundamental Theorem of Algebra
- Field Extensions as Vector Spaces
- Types of Field Extensions
- Nullstellensatz and Maximal Ideals
- Strong Nullstellensatz
- Galois Fields
- Normality and Separability
- Separable Extensions and Embeddings into Algebraic Closures
- More Separability but over Finite Fields
- Eisenstein's Criterion and Cyclotomic Fields
- Field Extensions and the Automorphism Group
- Nth Cyclotomic Fields
- Simplicity of Extensions
- A Little Galois Theory
- Galois Correspondence
- Galois Correspondence Failures
- Cyclic Galois Groups, Characters and Lie Brackets
- Applications of Galois Theory
- Fundamental Theorem for Symmetric Polynomials
- Tensor Products
- Preliminary Category Theory
- Tensor Products and Hom Adjunction
- Universal Properties
- Extension/Restriction of Scalars (Base Change)
- Tor Functor, Exactness, Flatness
- Multilinear Maps
- The Determinant, a top exterior power
- Projective Modules
- The Ext Functors
- Injective Modules