Design theory is a well-established branch of combinatorial mathematics. The origins of the subject can be traced back to statistics in the pioneering works of R. A. Fisher, F. Yates, and R. C. Bose. From the very beginning, one of the central objects of design theory has been symmetric designs. The prototype of a symmetric design is a finite projective plane, and the theory of symmetric designs borrows its methods and ideas from finite geometries, group theory, number theory, and linear algebra.

It is notoriously difficult to construct an infinite family of symmetric designs or even a single symmetric design. However, in recent years new ideas in constructing symmetric designs have been discovered and new infinite families have been found. The central role in these constructions is played by balanced generalized weighing matrices. These matrices generalize the notion of a symmetric design but until recently they were often regarded as a rather obscure combinatorial object. Now they seem to be a useful tool in unifying different construction methods that have been developed since the 1950s.

This book is primarily a research monograph which aims to give a unifying exposition of the theory of symmetric designs with emphasis on these new developments. The book covers the combinatorial aspects of the theory with particular attention to constructing symmetric designs and related objects. Recent results that have never previously appeared in book format are developed mainly in the last five chapters.