Groups
- Series of groups (Jordan-Holder Theorem), solvable and nilpotent groups
- Representation theory (Maschke's Theorem)
Rings
- Modules
- Division rings (Wedderburn's Theorem)
- Noetherian rings (Hilbert Basis Theorem, power series rings), localization
- Semi-simple rings (Density Theorem)
- Gröbner Bases
- Affine algebraic varieties
Fields
- Separable, inseparable and purely inseparable extensions, normal extensions
- Transcendental extensions (transcendence bases)
- Galois theory
References
Dummit and Foote: Abstract Algebra
Hungerford: Algebra
Lang: Algebra
Rotman: Advanced Modern Algebra
