  In these lecture notes I review the theory of the non--linear evolution of
cosmological perturbations in a self--gravitating collisionless medium, with
vanishing vorticity. The problem is first analyzed in the context of the
Newtonian approximation, where the basic properties of the Zel'dovich,
frozen--flow and adhesion algorithms are introduced. An exact general
relativistic formalism is then presented and it is shown how the Newtonian
limit, both in Lagrangian and Eulerian coordinates, can be recovered. A general
discussion on the possible role of possible relativistic effects in the
cosmological structure formation context is finally given.
