  We present a construction of all finite indecomposable involutive solutions
of the Yang-Baxter equation of multipermutational level at most 2 with abelian
permutation group. As a consequence, we obtain a formula for the number of such
solutions with a fixed number of elements. We also describe some properties of
the automorphism groups in this case - in particular, we show they are regular
abelian groups.
