  Consider a sequence of pointed n-dimensional complete Riemannian manifolds
{(M_i,g_i(t), O_i)} such that t in [0,T] are solutions to the Ricci flow and
g_i(t) have uniformly bounded curvatures and derivatives of curvatures. Richard
Hamilton showed that if the initial injectivity radii are uniformly bounded
below then there is a subsequence which converges to an n-dimensional solution
to the Ricci flow. We prove a generalization of this theorem where the initial
metrics may collapse. Without injectivity radius bounds we must allow for
convergence in the Gromov-Hausdorff sense to a space which is not a manifold
but only a metric space. We then look at the local geometry of the limit to
understand how it relates to the Ricci flow.
