William Thurstons ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The purpose of the present volume and of the other volumes in the same series is to provide a collection of articles that allows the reader to learn the important aspects of Thurstons heritage. The topics covered in this volume include Kleinian groups, holomorphic motions, earthquakes from the Anti-de Sitter point of view, the Thurston and WeilPetersson metrics on Teichmüller space, 3-manifolds, geometric structures, dynamics on surfaces, homeomorphism groups of 2-manifolds and the theory of orbifolds.

Kenichi Ohshika is a professor of mathematics at Gakushuin University, and a professor emeritus at Osaka University. He receivedhis PhD from the University of Tokyo in 1989, and worked at Tokyo Institute of Technology, University of Tokyo, and Osaka University before joining Gakushuin University. His interests includes Kleinian groups, hyperbolic geometry, Teichmüller theory, and 3-manifolds. He has held visiting positions at Institut des Hautes Études Scientifiques (1990-1991, 1999-2000), University of Warwick (1988-89, 1993, 2007), Université de Montréal (1995), Hausdorff Research Institute of Mathematics (2010), Université de Strasbourg (2014, 2019) and the Korea Institute of Advanced Science (2009-2015). He is a recipient of the MSJ geometry prize (2012), and the author of more than 60 papers.

Athanase Papadopoulos (born 1957) is Directeur de Recherche at the French Centre National de la Recherche Scientifique. His main fields of interest are geometry andtopology, the history and philosophy of mathematics, and mathematics and music. He has held visiting positions at the Institute for Advanced Study, Princeton (198485 and 199394), USC (19981999), CUNY (Ada Peluso Professor, 2014), Brown University (Distinguished visiting professor, 2017), Tsinghua University, Beijing (2018), Lamé Chair of the State University of Saint Petersburg (2019), and has had several month visits to the Max-Plank Institute for mathematics (Bonn), the Erwin Schrödinger Institute (Vienna), the Graduate Center of CUNY (New York), the Tata Institute (Bombay), Galatasaray University (Istanbul), the University of Florence (Italy), Fudan University (Shanghai), Gakushuin University (Tokyo) and Presidency University (Calcutta). He is the author of more than 200 published articles and 35 monographs and edited books.

1 Kenichi Ohshika and Athanase Papadopoulos: Introduction.- 2 Huiping Pan and Weixu Su: The geometry of the Thurston metric: a survey.- 3 Binbin Xu: Thurston's metric on the Teichmüller space of flat tori.- 4 Farid Diaf and Andrea Seppi: The Anti-de Sitter proof of Thurston's earthquake theorem.- 5 Nicholas Vlamis: Homeomorphism groups of self-similar 2-manifolds.- 6 Eric Schippers and Wolfgang Staubach: Weil-Petersson Teichmüller theory of surfaces of infinite conformal type.- 7 Hiroshige Shiga and Toshiyuki Sugawa: Kleinian groups and geometric function theory.- 8 Ken'ichi Ohshika: Thurston's broken windows only theorem revisited.- 9 Christoforos Neofytidis: Geometric structures in Topology, Geometry, Global Analysis and Dynamics.- 10 Jayadev Athreya: Counting problems for invariant point processes.- 11 Juan Martin Pérez and Florent Schaffhauser: Orbifolds and the modular curve.- 12 Athanase Papadopoulos: On Thurston's notes on the Geometry and Topology of 3-manifolds.