Introduction to geometry, dynamics, and moduli in low dimensions - LMS-CMI Research School 2017

Under construction!

Some references (survey papers and lecture notes)

Howard Masur - Ergodic theory of translation surfaces,
   Handbook of Dynamical Systems, Vol. 1B pdf

Alex Wright - Translation surfaces and their orbit closures: An introduction for a broad audience,
   EMS Surv. Math. Sci. 2015 pdf

Giovani Forni and Carlos Matheus - Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards,
   ArXiV pdf

Sebastien Gouëzel and Erwan Lanneau - Un théorème de Kerckhoff, Masur et Smillie : Unique ergodicité sur les surfaces plates,
   Séminaires et Congrès 20 (2010) pdf

Howard Masur and Serge Tabachnikov - Rational billiards and flat structures,
   Handbook of dynamical systems, Vol. 1A, North-Holland, Chapter 13 (2002) dvi | pdf (with figures).

Marcelo Viana - Dynamics of interval exchange maps and Teichmüller flows,
   Lecture notes of graduate courses taught at IMPA in 2005 and 2007 pdf.

Martin Möller - Affine groups of flat surfaces,
   Handbook of Teichmüller Theory, Volume 2, Chapter 10 pdf.

Martin Möller -Teichmüller curves from an algebraic viewpoint,
   Park City Lecture notes (2011) pdf.

John Smillie -The dynamics of billiard flows in rationnal polygons,
   Dynamical System Ergodic Theory and Applications (2000) pdf.

John Smillie and Barak Weiss - Finiteness results for flat surfaces: a survey and problem list,
   Proceedings of a conference, Fields Institute, Toronto (2006) pdf.

Yaroslav Vorobets - Planar structures and billiards in rational polygons: the Veech alternative,
   Russian Mathematical Surveys pdf.

Jean-Christophe Yoccoz - Échanges d'Intervalles et Surfaces de Translation,
   Séminaire BOURBAKI 60ème année, 2007-2008, no 996 (2008) pdf.

Jean-Christophe Yoccoz - Interval exchange maps and translation surfaces,
   Pisa Lectures (2007) pdf.

Jean-Christophe Yoccoz - Échanges d'Intervalles,
   Cours au Collège de France (2005) pdf. See also Matheus's Weblog.

Jean-Christophe Yoccoz - Cours et séminaires au Collège de France,
   Page du Collège de France html.

(Some) Previous schools

Les Houches School: Frontiers in Number Theory, Geometry and Physics, proceedings of the Spring School at Les Houches (2003)
Anton Zorich - Flat surfaces pdf.
Jean-Christophe Yoccoz - Continued Fraction Algorithms for Interval Exchange Maps: an Introduction pdf.

Luminy (2003): Handbook of Dynamical Systems (Vol 1, Part B, 2006):
Pascal Hubert and Thomas Schmidt - Chapter 6: An introduction to veech surfaces pdf.
Howard Masur - Chapter 7: Ergodic Theory of Translation surfaces pdf.
Giovanni Forni - Chapter 8: On the lyapunov exponents of the Kontsevich-Zorich cocycle pdf.
Alex Eskin - Chapter 9: Counting problems in moduli space pdf.

Problem lists

P. Hubert, H. Masur, T. Schmidt and A. Zorich - Problems on billiards, flat surfaces and translation surfaces,
   Problems on Mapping Class Groups and Related Topics Proc. Sympos. Pure Math., 74, Amer. Math. Soc., Providence, RI, (2006) pdf.

J. Smillie and B. Weiss - Finiteness results for flat surfaces: a survey and problem list,
   Partially hyperbolic dynamics, laminations, and Teichmüller flow Proceedings of a conference, Fields Institute, Toronto (2006) pdf.

EXERCISES

Alex Wright - EXERCISES TO ACCOMPANY TRANSLATION SURFACES AND THEIR ORBIT CLOSURES,
   pdf.
More lectures on Alex's web page: here.

Vincent Delecroix and Samuel Lelievre - School at Morelia,
   here.