Peter Schneider is a professor in the Mathematical Institute at the University of Münster. His research interests lie within the Langlands program, which relates Galois representations to representations of p-adic reductive groups, as well as in number theory and in representation theory. He is the author of Nonarchimedean Functional Analysis (2001), p-Adic Lie Groups (2011) and Modular Representation Theory of Finite Groups (2012), and he is a member of the National German Academy of Science Leopoldina and of the Academia Europaea.

• Preface; Overview; 1. Relevant constructions; 2. (ϕL, ΓL-modules); 3. An equivalence of categories; 4. Further topics; References; Notation; Subject index.

'Much of this material is available in the literature, but it has never been presented so cleanly and concisely in a single place before … In this book, Schneider has done a remarkable job of displaying the beauty and power of perfectoid theoretic techniques. His text is sure to occupy and satisfy the attention of students and researchers working on Galois representations, or those who suspect that perfectoid-style techniques might be relevant for their work. We recommend Schneider's text to anyone with even a passing interest in the perfectoid revolution initiated by Scholze.' Cameron Franc, Mathematical Reviews