INTEGRABLE 1+1 DIMENSIONAL GRAVITY MODELS

Integrable models of dilaton gravity coupled to electromagnetic and sc alar matter fields in dimensions 1+1 and 0+1 are reviewed. The 1+1 dim ensional integrable models are either solved in terms of explicit quad ratures or reduced to the classically integrable Liouville equation. T he 0+1 dimensional integrable models emerge as sectors in generally no n integrable 1+1 dimensional models and can be solved in terms of expl icit quadratures. The Hamiltonian formulation and the problem of quant izing are briefly discussed. Applications to gravity in any space-time dimension are outlined and a generalization of the so called 'no-hair ' theorem is proven using local properties of the Lagrange equations f or a rather general 1+1 dimensional dilaton gravity coupled to matter.