Abstract: I wish to explain the work by Fock (jr) "Dual Teichmuller space". It is known that any Riemann surface is a quotient of the Lobachevski plane modulo a discrete group of isometries. Fock presents an explicit description of such groups (in terms of 2x2-matrices and writes the action ogf the mapping class group (diffeomorphism of a Riemann surface modulo connected component) on the Teichmuller space.