The aim of this course is to introduce the Yang–Baxter equation, and how it arises as a sufficient condition for solvability of the lattice models of statistical mechanics. The related algebras of symmetries (called quantum groups) and their representation theory will be studied. Furthermore, we will discuss various interesting systems of difference–differential equations that are naturally associated with these representations. Time permitting, we will explain how the monodromy of these difference–differential equations ties various representation categories together. This event is part of the activities of the Excellence Department Project CUP B83C23001390001 and of the project PRIN2022HMBTTL Algebraic aspects of 2d-QFTs with reflection symmetry and it is funded by the European Union – Next Generation EU.