1 Teichmรผller Space of Genus g -- 1.1 Riemann Surfaces -- 1.2 Teichmรผller Space of Genus 1 -- 1.3 Teichmรผller Space of Genus g -- 1.4 Quasiconformal Mappings and Teichmรผller Space -- 1.5 Complex Structures and Conformal Structures -- Notes -- 2 Frike Space -- 2.1 Uniformization Theorem -- 2.2 Universal Coverings -- 2.3 Mรถbius Transformations -- 2.4 Fuchsian Models -- 2.5 Fricke Space -- Notes -- 3 Hyperbolic Geometry and Fenchel-Nielsen Coordinates -- 3.1 Poincarรฉ Metric and Hyperbolic Geometry -- 3.2 Fenchel-Nielsen Coordinates -- 3.3 Fricke-Klein Embedding -- 3.4 Thurstonโs Compactification -- Notes -- 4 Quasiconformal Mappings -- 4.1 Definitions and Elementary Properties -- 4.2 Existence Theorems on Quasiconformal Mappings -- 4.3 Dependence on Beltrami Coefficients -- 4.4 Proof of Calderรณn-Zygmund Theorem -- Notes -- 5 Teichmรผller Spaces -- 5.1 Analytic Construction of Teichmรผller Spaces -- 5.2 Teichmรผller Mappings and Teichmรผllerโs Theorerms -- 5.3 Proof of Teichmรผllerโs Uniqueness Theorem -- Notes -- 6 Complex Analytic Theory of Teichmรผller Spaces -- 6.1 Bersโ Embedding -- 6.2 Invariance of Complex Structure of Teichmรผller Space -- 6.3 Teichmรผller Modular Groups -- 6.4 Roydenโs Theorems -- 6.5 Classification of Teichmรผller Modular Transformations -- Notes -- 7 Weil-Petersson Metric -- 7.1 Petersson Scalar Product and Bergman Projection -- 7.2 Infinitesimal Theory of Teichmรผller Spaces -- 7.3 Weil-Petersson Metric -- Notes -- 8 Fenchel-Nielsen Deformations and Weil-Petersson Metric -- 8.1 Fenchel-Nielsen Deformations -- 8.2 A Variational Formula for Geodesic Length Functions -- 8.3 Wolpertโs Formula -- Notes -- Appendices -- A Classical Variations on Riemann Surfaces -- Notes -- B Compactification of the Moduli Space -- Notes -- References -- List of Symbols

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