  These notes are based on a series of lectures given by the author at the Max
Planck Institute for Mathematics in the Sciences in Leipzig. Addressed topics
include affine and projective toric varieties, abstract normal toric varieties
from fans, divisors on toric varieties and Cox's construction of a toric
variety as a GIT quotient. We emphasize the role of toric varieties in solving
systems of polynomial equations and provide many computational examples using
the Julia package Oscar.jl.
