  We consider the Ricci flow for simply connected nilmanifolds, which
translates to a Ricci flow on the space of nilpotent metric Lie algebras. We
consider the evolution of the inner product and the evolution of structure
constants, as well as the evolution of these quantities modulo rescaling. We
set up systems of O.D.E.'s for some of these flows and describe their
qualitative properties. We also present some explicit solutions for the
evolution of soliton metrics under the Ricci flow.
