we present a new compactness theory of ricci flows. this theory states that any sequence of ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. under a natural non-collapsing condition, this limiting flow is smooth on the complement of a singular set of parabolic codimension at least 4. we furthermore obtain a stratification of the singular set with optimal dimensional bounds depending 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 we obtain a description of the singularity formation at the first singular time and a long-time characterization of immortal flows, which generalizes the thick-thin decomposition in dimension 3. we also obtain a backwards pseudolocality theorem and discuss several other applications. \\ \\ the schedule of the lecture series will be approximately as follows: 1. heat kernel and entropy estimates on ricci flow backgrounds and related geometric bounds. 2. continuation of lecture 1 + synthetic definition of ricci flows (metric flows) and basic properties 3. convergence and compactness theory of metric flows 4. partial regularity of limits of ricci flows