The evolution of the large-scale structure of the universe: beyond the
  linear regime
  These lecture notes introduce analytical tools, methods and results
describing the growth of cosmological structure beyond the linear regime. The
presentation is focused on the single flow regime of the Vlasov-Poisson
equation describing the development of gravitational instabilities in a
pressureless fluid. These notes include the introduction of diagrammatic
representations of the standard perturbation theory with applications to the
calculation of the so-called loop contributions to the power spectra. A large
part of these notes is devoted to the exploration of the convergence properties
of these terms from the contribution of both the long-wave modes and the
short-wave modes. The resulting performances of the two-loop corrections of the
power spectra are then presented. Finally other avenues that use different
methods are explored. In particular it is shown how joint density and profile
probability distribution functions can be constructed out of the
multiple-variable cumulant generating functions computed at tree order.
