The extraordinary and astonishing idea of making a statistical inference by shuffling treatment labels, whilst conditioning on the actual values observed, is associated in particular with R A Fisher. However, it turns out to have a rich and fascinating history beyond the contributions of The Master of Inference and this is wonderfully recounted in this impressive monograph. The book is a tour de force. It manages the difficult trick of being authoritative and comprehensive but also entertaining. Two expert veterans of the field of permutation methods, Paul Mielke and Kenneth Berry have been joined by a younger scientist, Janice Johnston, to produce a book that works not only as a first-rate reference but also as a readable history of statistics and, incidentally, of advances in computing.