  In this paper we characterize non-collapsed limits of Ricci flows. We show
that such limits are smooth away from a set of codimension $\geq 4$ in the
parabolic sense and that the tangent flows at every point are given by gradient
shrinking solitons, possibly with a singular set of codimension $\geq 4$. We
furthermore obtain a stratification result of the singular set with optimal
dimensional bounds, which depend on the symmetries of the tangent flows. Our
methods also imply the corresponding quantitative stratification result and the
expected $L^p$-curvature bounds.
  As an application of our theory, we obtain a description of the singularity
formation of a Ricci flow at its first singular time and a thick-thin
decomposition characterizing the long-time behavior of immortal flows. These
results generalize Perelman's results in dimension 3 to higher dimensions. We
also obtain a Backwards Pseudolocality Theorem and discuss several other
applications.
