  We prove that the Gromov boundary of every hyperbolic group is homeomorphic
to some Markov compactum. Our reasoning is based on constructing a sequence of
covers of $\partial G$, which is quasi-$G$-invariant wrt. the ball $N$-type
(defined by Cannon) for $N$ sufficiently large. We also ensure certain
additional properties for the inverse system representing $\partial G$, leading
to a finite description which defines it uniquely.
  By defining a natural metric on the inverse limit $\lim K_n$ and proving it
to be bi-Lipschitz equivalent to an accordingly chosen visual metric on
$\partial G$, we prove that our construction enables providing a simplicial
description of the natural quasi-conformal structure on $\partial G$. We also
point out that the initial system of covers can be modified so that all the
simplexes in the resulting inverse system are of dimension less than or equal
to $\dim \partial G$.
  We also generalize --- from the torsion-free case to all finitely generated
hyperbolic groups --- a theorem guaranteeing the existence of a finite
representation of $\partial G$ of another kind, namely a semi-Markovian
structure (which can be understood as an analogue of the well-known automatic
structure of $G$ itself).
