We present a unified approach to the study of the asymptotic behavior of ergodic averages (speed of ergodicity, deviation of ergodic averages) for a few basic examples of parabolic flows (suspensions of interval exchange transformations, horocycle flows and some nilflows). The method is based on the study of a renormalization cocycle on a bundle of distributions (or currents) invariant under the dynamics and on estimates on solutions of cohomological equations. The plan of the lectures is the following: We formulate a notion of algebraic renormalization, which is sufficiently general to cover all known examples of ”algebraic” renormalizable flows (linear toral flows, horocycle flows on surfaces of constant curvature, suspensions of interval exchange transformation) and to suggest a new example (Heisenberg nilflows). We briefly discuss the limitations of this notion and possible generalizations. We then outline the basic features of cohomological equations in the parabolic uniquely ergodic examples under consideration (versus the elliptic and the hyperbolic case), in particular the presence of distributional obstructions to the existence of solutions and describe the renormalization cocycle (over the renormalization dynamics) relevant to the deviation of ergodic averages. Finally, we explained our method at work in the case of suspensions of interval exchange transformations and of Heisenberg nilflows (with applications to number theory). Coauthor: Livio Flaminio (Univ. Lille, France)