These lecture notes correspond to my youtube lecture series which can be found here.

- Introduction – definition of rings and examples.
- Introduction – basic definitions and properties.
- The quaternions – the noncommutative field example.
- Subrings and generating sets.
- Homomorphisms.
- Ideals and quotient rings.
- Isomorphism theorems.
- The Chinese Remainder Theorem.
- Approximating rings.
- Maximal ideals.
- Fraction fields and prime ideals.
- Euclidean domains.
- Principal ideal domains.
- Unique factorization domains.
- Gaussian integers.
- Polynomials over unique factorization domains.
- Irreducible polynomials.
- Polynomials over fields.
- Introduction to fields.
- Algebraic extensions.
- Towers of fields.
- Finite fields.
- Subfields of finite fields.
- The multiplicative group of a field.