Elliptic hypergeometric functions

Book chapter, 2020

Lecture notes for a course given at the summer school OPSF-S6, College Park, Maryland, 11-15 July 2016. In these lecture notes I give an elementary introduction to elliptic hypergeometric functions. I focus on motivating the main ideas and constructions, rather than giving a comprehensive survey. The lectures include a brief explanation of the historical origin of elliptic hypergeometric functions in the context of solvable lattice models. In particular, I give a new proof of the fact that fused Boltzmann weights for the elliptic solid-on-solid model can be expressed as elliptic hypergeometric sums.