Basic Algebraic Geometry: In this part, we introduce Spec(R) and affine semigroups. This allows us to give yet another characterization of affine toric varieties in terms of affine semigroups.

1. Toric Varieties 1 - Affine Varieties over C
2. Toric Varieties 2 - Affine Toric Varieties
3. Toric Varieties 3 - Coordinate Rings and Morphisms
4. Toric Varieties 4 - Spec(R) and Affine Semigroups
5. Toric Varieties 5 - Polyhedral Cones for Affine Toric Varieties
6. Toric Varieties 6 - Faces and Localization
7. Toric Varieties 7 - Overview of Smoothness and Normality
8. Projective Toric Varieties - Part 1
9. Projective Toric Varieties - Part 2
10. Affine Pieces of Projective Toric Varieties

In this short series of 10 lessons, Dr. Bob explains the fundamentals of algebraic geometry, including toric varieties, coordinate rings, morphisms, faces, localization, smoothness, normality, and much more.