- SOME PRELIMINARY RESULTS
- Automorphisms of certain domains in the Riemann sphere
- Möbius transformations
- Kleinian and Fuchsian groups
- Hyperbolic metrics
- Quasiconformal mappings
- Beltrami differentials for groups
- Automorphic forms and quadratic differentials on surfaces
- Nielsen's theorem

- TEICHMÜLLERTHEORY
- The Riemann Mapping Theorem and the Uniformization Theorem
- Abel's theorem and the uniformization of tori
- Teichmüller spaces of Riemann surfaces, moduli spaces and modular groups
- Teichmüller spaces of Fuchsian groups
- Fricke coordinates
- Teichmüller's theorem
- Teichmüller's lemma and the complex structure of Teichmüller spaces
- Bers embedding and the Bers boundary of Teichmüller space
- Royden's Theorems
- The Patterson and Bers-Greenberg Isomorphism Theorems
- The Weil-Petersson metric

- THURSTON'S THEORY
- Thurston's approach to Teichmüller spaces and diffeomorphisms of surfaces
- Bers' and Thurston's compactifications of Teichmüller space
- Bers' approach to Thurston's classification of diffeomorphisms of surfaces

- SOME RESULTS ON THE WEIL-PETERSSON METRIC
OF TEICHMÜLLER SPACES
- The pants and curve complexes of a surface
- The pants complex and Teichmüller space are quasi-isometric
- Linear growth of infinite order mapping class group elements
- Isometries of the Weil-Petersson metric
- Gromov-hyperbolicity
- The Weil-Petersson visual sphere
- 3-manifolds and the Weil-Petersson distance

- Bibliography

These notes were written for some expository talks on Teichmüller theory, given
at Conference on Low-dimensional manifolds and Groups

,
held in the Indian Statistical Institute, Bangalore, July 12-24, 2004.
I have tried to make §§3 and 4 a little independent from §§1 and 2
(if one has a little background in the theory) and of each other. So
some definitions might appear in §3 and also in §4.

The notes are far from complete, proofs are not given; they are meant as a guide for lecturing, rather than a formal introduction to the theory of Teichmüller spaces.

Pablo Ares Gastesi 2005-08-31