In this chapter, we recall the classic classification of finite solvable primitive groups. We study indecomposable solutions to the YBE and show that homomorphic images of indecomposable solutions are also indecomposable. We introduce simple solutions to the YBE and show that for cardinalities greater than 2, they are indecomposable. Furthermore, the simple solutions of non-prime cardinalities are irretractable. We continue with the classification of the finite primitive involutive solutions. Finally, we provide some methods to construct simple involutive solutions.