Groups, Radical Rings, and the Yang-Baxter Equation: A Combinatorial Approach to Solutions

This monograph provides the first comprehensive introduction to set-theoretic solutions of the Yang–Baxter equation and their deep connections with skew braces. In recent decades, set-theoretic solutions have emerged as an accessible yet rich domain of study, offering new algebraic structures and revealing unexpected connections between seemingly distant fields. A key breakthrough in this direction was the discovery of braces by Rump and the later generalization to skew braces, which provid...