**Lecture 1 (1/21/2021)**: Presheaves and sheaves on topological spaces

**Lecture 2 (1/28/2021)**: Locally ringed spaces and the inevitibility of schemes

**Lecture 3 (2/4/2021)**: Schemes

**Lecture 4 (2/11/2021)**: Gluing schemes, Proj

**Lecture 5 (2/18/2021)**: More about Proj, some properties of schemes and morphisms

**Lecture 6 (2/25/2021)**: Fiber products, separated and proper morphisms

**Lecture 7 (3/4/2021)**: Separated and proper morphisms and the valuative criteria

**Lecture 8 (3/11/2021)**: Sheaves of modules, part 1: coherent and quasicoherent sheaves

**Lecture 9 (3/25/2021)**: Sheaves of modules, part 2: more about quasicoherent sheaves

**Lecture 10 (4/1/2021)**: Sheaves of modules, part 3: final comments

**Lecture 11 (4/8/2021)**: Divisors: Weil (and a bit of Cartier)

**Lecture 12 (4/15/2021)**: The many lives of divisors

**Lecture 13 (4/22/2021)**: Morphisms to projective space and ample invertible sheaves

**Lecture 14 (4/27/2021)**: Linear systems