Lecture notes:

Lecture 1: What are toric varieties?

Lecture 2: Lattices, Cocharacters and limit points, part I

Lecture 3: Cones and affine toric varieties, part I 

Lecture 4: Cones and affine toric varieties, part II

Lecture 5: Faces and opens, fans and toric varieties, part I

Lecture 6: Fans and toric varieties, more examples

Lecture 7: Toric ideals and monomial parametrizations

Lecture 8: Completeness and saturation, closed points of affine varieties, limit points part II

Lecture 9: Distinguished points are limit points, definitions of smoothness

Lecture 10: Finding all smooth affine toric varieties, definition of toric morphisms and first examples

Lecture 11: More examples of toric morphisms: blow-ups. Statement of resolution of singularities for toric surfaces.

Lecture 12: Proof of resolution of singularities for toric surfaces. Cyclic quotients.

Lecture 13: Cyclic quotients, cones over rational curves as cyclic quotients. Statement of the Orbit-Cone correspondence