  We study involutive non-degenerate set-theoretic solutions (X,r) of the
Yang-Baxter equation on a finite set X. The emphasis is on the case where (X,r)
is indecomposable, so the associated permutation group acts transitively on X.
One of the major problems is to determine how such solutions are built from the
imprimitivity blocks; and also how to characterize these blocks. We focus on
the case of so called simple solutions, which are of key importance. Several
infinite families of such solutions are constructed for the first time. In
particular, a broad class of simple solutions of order p^2, for any prime p, is
completely characterized.
