This book is a presentation of my recent research work into the theory and applications of mathematical relations between finite sets. The consequent results and concepts are expressed in 'conjunction' with the idea of a union of simplicial complexes and the algorithms and overall methodology have become known as Q-Analysis. The mathematical ideas are essentially comhinatorial and are developed in Section-A of the book, whilst Section-R contains an application to a community study (that of the IJniversity of Rssex). All of the work has been published elsewhere, in the usual form of papers, and a comprehensive introduction to the whole approach will be found in my earlier book, Mathematical Structure in Human Affairs (Heinemann, London 1974). Much of the research work referred to in this present hook would not have been possible without the co-operation of my research team, of whom I would particularly like to thank J.II. Johnson, and its puhlication owes a lot to the secretarial help provided by ~Iary Low. R.H. Atkin IJniversity of Rssex U.K.