  In this thesis we derive a hydrodynamical model to describe the dynamics of
density excitations localized at the edges of a Quantum Hall bar. In particular
we show that the chiral Luttinger liquid model for the edges excitations can be
derived from the coarse-graining and a lowest Landau level projection procedure
without reference to the Quantum Hall effect. We use this model to calculate
the Landauer-Buettiker conductances in generic experimental setups. In the
absence of tunneling the ideal Hall conductance is recovered. When the
tunneling between the edges is explicitely taken into account we obtain
expressions for the corrections to the ideal conductance. We discuss our result
vis-a-vis recent experiments in the weak tunneling regime and previous
theoretical models.
