In this learning seminar, we will define Calabi-Yau (CY) varieties, and give examples in low dimension, and explain some reasons why CY's

are important. Baytrev, in the early 1990's, gave a construction which produces a huge (yet finite) collection of CY 3-folds. In this talk we will describe this construction. It uses reflexive polytopes, fans and (projective) toric varieties. You do not need to know all of these things for this learning seminar. We will do the construction via examples so you can see the construction in action and understand how the geometry and discrete polyhedral data interact.