  We explicitly describe the Teichmuller space TH_n of hyperelliptic surfaces
in terms of natural and effective coordinates as the space of certain
(2n-6)-tuples of distinct points on the ideal boundary of the Poincare disc. We
essentially use the concept of a simple earthquake which is a particular case
of a Fenchel-Nielsen twist deformation. Such earthquakes generate a group that
acts transitively on TH_n. This fact can be interpreted as a continuous analog
of the well-known Dehn theorem saying that the mapping class group is generated
by Dehn twists. We find a simple and effective criterion that verifies if a
given representation of the surface group \pi_1\Sigma in the group of
isometries of the hyperbolic plane is faithful and discrete. The article also
contains simple and elementary proofs of several known results, for instance,
of W. M. Goldman's theorem [Gol1] characterizing the faithful discrete
representations as having maximal Toledo invariant (which is essentially the
area of the representation in the two-dimensional case).
