Foreword ...................................................... vii
Introduction to Teichmüller theory, old and new, IV
by Athanase Papadopoulos ..................................... 1
Part A. The metric and the analytic theory, 4
Chapter 1. Local and global aspects of Weil-Petersson
geometry
by Sumio Yamada ............................................. 43
Chapter 2. Simple closed geodesies and the study of
Teichmüller spaces
by Hugo Parlier ............................................ 113
Chapter 3. Curve complexes versus Tits buildings: structures
and applications
by Lizhen Ji ............................................... 135
Chapter 4. Extremal length geometry
by Hideki Miyachi .......................................... 197
Chapter 5. Compactifications of Teichmüller spaces
by Ken'ichi Ohshika ........................................ 235
Chapter 6. Arc geometry and algebra: foliations, moduli
spaces, string topology and field theory
by Ralph M. Kaufmann ....................................... 255
Chapter 7. The horoboundary and isometry group of Thurston's
Lipschitz metric
by Cormac Walsh ............................................ 327
Chapter 8. The horofunction compactification of the
Teichmüller metric
by Lixin Liu and Weixu Su .................................. 355
Chapter 9. Lipschitz algebras and compactifications of
Teichmüller space
by Hideki Miyachi .......................................... 375
Chapter 10. Asymptotically rigid mapping class groups and
Thompson's groups
by Zhong Li ................................................ 415
Chapter 11. Holomorphic families of Riemann surfaces and
monodromy
by Hiroshige Shiga ......................................... 439
Part B. Representation spaces and generalized structures, 2
Chapter 12. The deformation of flat affine structures on
the two-torus
by Oliver Baues ............................................ 461
Chapter 13. Higher Teichmüller spaces: from SL(2,  ) to
other Lie groups
by Marc Burger, Alessandra Iozzi, and Anna Wienhard ........ 539
Chapter 14. The theory of quasiconformal mappings in higher
dimensions, I
by Gaven J. Martin ......................................... 619
Part C. Dynamics
Chapter 15. Infinite-dimensional Teichmüller spaces and
modular groups
by Katsuhiko Matsuzaki ..................................... 681
Chapter 16. Teichmüller spaces and holomorphic dynamics
by Xavier Buff, Guizhen Cui, and Lei Tan ................... 717
Part D. The quantum theory, 2
Chapter 17. A survey of quantum Teichmüller space and
Kashaev algebra
by Ren Guo ................................................. 759
Part E. Sources
Chapter 18. Variable Riemann surfaces (translated from the
German by Annette A'Campo-Neuen)
by Oswald Teichmüller ...................................... 787
Chapter 19. A commentary on Teichmüller's paper
"Veränderliche Riemannsche Flächen"
by Annette A'Campo-Neuen, Norbert A'Campo, Lizhen Ji,
and Athanase Papadopoulos .................................. 805
List of Contributors .......................................... 815
Index ......................................................... 837
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