  Gravitational and electrostatic interactions are fundamental examples of
systems with long-range interactions. Equilibrium properties of simple models
with long-range interactions are well understood and exhibit exotic behaviors :
negative specific heat and inequivalence of statistical ensembles for instance.
  The understanding of the dynamical evolution in the case of long-range
interacting systems still represents a theoretical challenge. Phenomena such as
out-of-equilibrium phase transitions or quasi-stationary states have been found
even in simple models.
  The purpose of the present thesis is to investigate the dynamical properties
of systems with long-range interactions, specializing on one-dimensional
models. The appropriate kinetic description for these systems is the Vlasov
equation. A numerical simulation tool for the Vlasov equation is developed.
  A detailed study of the out-of-equilibrium phase transition occuring in the
Free-Electron Laser is performed and the transition is analyzed with the help
of Lynden-Bell's theory.
  Then, the presence of stretching and folding in phase space for the
Hamiltonian Mean-Field model is studied and quantified from the point of view
of fluid dynamics. Finally, a system of uncoupled pendula for which the
asymptotic states are similar to the ones of the Hamiltonian Mean-Field model
is introduced. Its asymptotic evolution is predicted via both Lynden-Bell's
theory and an exact computation. This system displays a fast initial evolution
similar to the violent relaxation found for interacting systems. Moreover, an
out-of-equilibrium phase transition is found if one imposes a self-consistent
condition on the system.
  In summary, the present thesis discusses original results related to the
occurence of quasi-stationary states and out-of-equilibrium phase transitions
in 1D models with long-range interaction.
