**Algebra**

- Intuition, analogies and abstraction
- Ring theory I: Motivating ring theory, domains with integer-polynomial analogies
- Ring theory II: Visualizing various domains
- Group theory I: Presentations and representations
- Group theory II: Visualizing non-abelianness, normality and group products
- Galois theory I: Walkthrough of Galois theory
- Galois theory II: Essence of the Galois correspondence
- Galois theory III: Polynomials seen more generally
- Homomorphism theorems and a primer on category theory

**Algebraic geometry**

- Introduction to Algebraic Geometry
- Bezout's identity [3]
- Zariski topology [1][2]
- Nullstellensatz problem
- Spectrum; rings seen more generally

**Algebraic number theory**

- Number theory: Part I
- Class field theory, reciprocity laws, factorization of ideals
- Group characters and reciprocity laws
- Mordell equations
- p-adic numbers

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