Association schemes are of interest to both mathematicians and statisticians and this book was written with both audiences in mind. For statisticians, it shows how to construct designs for experiments in blocks, how to compare such designs, and how to analyse data from them. The reader is only assumed to know very basic abstract algebra. For pure mathematicians, it tells why association schemes are important and develops the theory to the level of advanced research. This book arose from a course successfully taught by the author and as such the material is thoroughly class-tested. There are a great number of examples and exercises that will increase the book's appeal to both graduate students and their instructors. It is ideal for those coming either from pure mathematics or statistics backgrounds who wish to develop their understanding of association schemes.

Review of the hardback:‘As expected, Rosemary Bailey has presented us with a very scholarly work. She successfully draws the two threads of experimental design and the pure mathematics of association schemes together in this extremely thorough exposition … The author has made an important contribution to bridging the gap between these two areas.‘Short Book Reviews

Review of the hardback:‘This book sets out on a very ambitious course, to bring these two groups together. it succeeds admirably … One might feel that a reader interested only in designed experiments, or conversely only in algebraic combinatorics, may find the union of the two more difficult. However, the book is written so that both types of reader will find the presentation engaging; indeed one cannot help but conclude that these two viewpoints belong together. The author has done the community a valuable service by strengthening a link between the two.‘Zentralblatt MATH

Review of the hardback:‘The author of this impressive monograph is well-known as a world leader who has made fundamental contributions to this field. Now she has come up with this elegantly written that provides a unified survey of the developments in and around association schemes. … lucid and well-organized, the book maintains a high level of mathematical rigour and depth. The impressive list of references, including the most up-to-date ones, will make the book particularly valuable. The large number of examples and exercises, all meticulously chosen, will certainly endear the book to its readers. The author has done a tremendous job, and the scientific community will be the beneficiary. This marvellous book should find a place in the bookshelf of any serious researcher in experimental design and combinatorial theory.‘Indian Journal of Statistics

Review of the hardback:‘… a valuable contribution to one of the important aspects of commutative scheme theory: the application of commutative scheme theory to statistics. … fills one of the many gaps in the global view of schemes and their central role in mathematics.‘Bulletin of the American Mathematical Society

Review of the hardback:'… a welcome addition to researchers in the area of association schemes as it is comprehensive and indicates likely directions for future work.'Journal of the Royal Statistical Society, Series A