Indecomposable involutive set-theoretical solutions to the Yang-Baxter equation of size $p^2$

This article focuses on indecomposable involutive non-degenerate set-theoretical solutions to the Yang–Baxter equation. More specifically, we give a full classification of those solutions which are of size $p^2$, for $p$ a prime. We do this through a thorough analysis of their associated permutation braces and using the language of cycle sets.