  All known examples of nontrivial homogeneous Ricci solitons are
left-invariant metrics on simply connected solvable Lie groups whose Ricci
operator is a multiple of the identity modulo derivations (called solsolitons,
and nilsolitons in the nilpotent case). The tools from geometric invariant
theory used to study Einstein solvmanifolds, turned out to be useful in the
study of solsolitons as well. We prove that, up to isometry, any solsoliton can
be obtained via a very simple construction from a nilsoliton together with any
abelian Lie algebra of symmetric derivations of its metric Lie algebra. The
following uniqueness result is also obtained: a given solvable Lie group can
admit at most one solsoliton up to isometry and scaling. As an application,
solsolitons of dimension at most 4 are classified.
