Beginning with sets, functions, and relations, we will see how we are tempted to introduce category theory. After defining the data structures for categories, we will examine some examples. A functor is a function from one category to another that preserves the data structures of the source in its image. Given two categories and two functors between them, a natural transformation is used to compare how the two functors preserve data structures. We will see polymorphic functions in Haskell are natural transformations.