  This work hopes to be an introduction to Deligne categories for someone
familiar with classical representation theory and some category theory. In the
first chapter, we motivate and define (symmetric) tensor categories, construct
the Deligne categories, and prove their universal properties. In the second
chapter, we define ultraproducts and use them to construct the Deligne
categories in a different way; in particular, this construction works in
positive characteristic. In the third chapter, we connect Deligne categories to
the classical categories by discussing simple objects and explaining what
happens in the $t = n$ case. In the last chapter, along with recommendations
for further and related reading, we give an example of an investigation of
Harish-Chandra bimodules in representation theory in complex rank, which is a
joint work with Alexandra Utiralova (arXiv:2107.03173).
