Toric varieties is a topic in algebraic geometry with deep connections to polytopes, polyhedra, combinatorics, commutative algebra, symplectic geometry and topology. This course will serve as an introduction to algebraic geometry and polyhedral geometry by introducing the standard material on toric varieties (cones, fans, polytopes; affine, projective, and abstract toric varieties; divisors and cohomology). If time permits some further topics will be discussed. We will follow the textbook Toric Varieties by D. Cox, J. Little and H. Schenck. Prerequisites: Math 5031 and Math 5032.