Finite dimensional Teichmüller spaces and generalizations

Background 1. Introduction 2. Teichmuller spaces and modular groups 3. Teichmüller's theorem 4. Real boundaries 5. Classification of modular transformations 6. Embedding into complex number space 7. Metrics in Teichmuller space 8. Quasi-Fuchsian groups 9. Fiber spaces over Teichmuller spaces 10.Complex boundaries 11. 6-groups 12. Ahlfors' problem, Sullivan's theorem and the complex boundary 13.The Maskit embedding 14.Riemann surfaces with nodes 15.Strong deformation spaces 16.Complex structure of deformation spaces 17.Moduli spaces APPENDIX 18.Some auxiliary results.19.Infinite dimensional Teichmuller spaces References Background.(A) This paper is an expanded version of one read at the Poincaré Symposium of the American Mathematical Society at Bloomington, Indiana, in April 1980.The subject belongs to the "higher" theory of Riemann surfaces, and some readers may not object to being reminded of the main facts in the "standard" theory.A Riemann surface S is a connected surface on which one can do complex function theory which is, locally, not distinguishable from ordinary complex function theory in a domain of the complex number plane C.More precisely, it is required that S be a connected Hausdorff space, that certain continuous complex valued functions on subdomains of S be designated as holomorphic, and that the following propositions be valid, (i) For every point P of S there