The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solution. It also treats the regularity of solution of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solution of the Vlasov-Poisson system of particles under the self-induced gravitational/elecrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.