Preface. (Ken'ichi Ohshika and Athanase Papadopoulos).- Introduction. (Ken'ichi Ohshika and Athanase Papadopoulos).- Chapter 1: A glimpse into Thurston's work. (Ken'ichi Ohshika and Athanase Papadopoulos).- Chapter 2: Thurston's influence on Japanese topologists up to the 1980s. (Ken'ichi Ohshika).- Chapter 3: A survey of the impact of Thurston's work on Knot Theory. (Makoto Sakuma).- Chapter 4: Thurston's theory of 3-manifolds. (Sadayoshi Kojima).- Chapter 5: Combinatorics encoding geometry: The legacy of Bill Thurston in the story of one theorem. (Philip Bowers).- Chapter 6: On Thurston's parameterization of CP1-structures. (Shinpei Baba).- Chapter 7: A short proof of an assertion of Thurston concerning convex hulls. (Graham Smith).- Chapter 8: The double limit theorem and its legacy. (Cyril Lecuire).- Chapter 9: Geometry and topology of geometric limits. I. (Ken'ichi Ohshika and Teruhiko Soma).- Chapter 10: Laminar groups and 3-manifolds. (Hyungryul Baik and KyeongRo Kim).- Chapter 11: Length functions on currents and applications to dynamics and counting. (Viveka Erlandsson and Caglar Uyanik).- Chapter 12: Big mapping class groups: an overview. (Javier Aramayona and Nicholas Vlamis).- Chapter 13: Teichm uller theory, Thurston theory, Extremal length geometry and Complex analysis. (Hideki Miyachi).- Chapter 14: Signatures of monic polynomials. (Norbert A'Campo).- Chapter 15: Anti-de Sitter geometry and Teichm uller theory. (Francesco Bonsante and Andrea Seppi).- Chapter 16: Quasi-Fuchsian co-Minkowski manifolds. (Thierry Barbot and Francois Fillastre).