  We present a description of the moduli space of holomorphic vector bundles
over Riemann curves as a double coset space which is differ from the standard
loop group construction. Our approach is based on equivalent definitions of
holomorphic bundles, based on the transition maps or on the first order
differential operators. Using this approach we present two independent
derivations of the Hitchin integrable systems. We define a "superfree" upstairs
systems from which Hitchin systems are obtained by three step hamiltonian
reductions. A special attention is being given on the Schottky parameterization
of curves.
