  Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of
mathematical physics, algebra and combinatorics. Such a solution consists of a
set $X$ and a function r:X x X --> X x X which satisfies the braid relation.
  We examine solutions here mainly from the point of view of finite permutation
groups: a solution gives rise to a map from $X$ to the symmetric group $Sym(X)$
on $X$ satisfying certain conditions.
  Our results include many new constructions based on strong twisted union and
wreath product, with an investigation of retracts and the multipermutation
level and the solvable length of the groups defined by the solutions and new
results about decompositions and factorisations of the groups defined by
invariant subsets of the solution.
