  Toric varieties are perhaps the most accessible class of algebraic varieties.
They often arise as varieties parameterized by monomials, and their structure
may be completely understood through objects from geometric combinatorics.
While accessible and understandable, the class of toric varieties is also rich
enough to illustrate many properties of algebraic varieties. Toric varieties
are also ubiquitous in applications of mathematics, from tensors to statistical
models to geometric modeling to solving systems of equations, and they are
important to other branches of mathematics such as geometric combinatorics and
tropical geometry.
  These notes are based on, and significantly extend, Frank Sottile's short
course of four lectures at the CIMPA school on Combinatorial and Computational
Algebraic Geometry in Ibadan, Nigeria 12--23 June 2017.
