This impressive volume (in size, since it is almost 800 pages, and for the number and level of contributions) consists of a collection of texts on several topics, gathered to commemorate the 80th birthday of Prof. John W. Milnor. In February 2011, there was a conference at the Banff Centre (Canada) on holomorphic dynamics in one and several variables and other topics related to the work of John Milnor. John Milnor is undoubtedly one of the most significant mathematicians of the second half of the twentieth century. He has made fundamental discoveries in many areas of modern mathematics, including topology, geometry, K-theory, and dynamical systems. This book is an outgrowth of that conference. It comprises surveys and papers inspired by Milnor's work, from experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself.

The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vicente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky.

The volume is organized in five main parts: I. One Complex Variable, II. One Real Variable, III. Several Complex Variables, IV. Laminations and Foliations, V. Geometry and Algebra, each of which consists of the contributions falling in such field. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This book is certainly useful to students and researchers in complex dynamics and related fields.