Permanents made their first appearance in 1812 in the famous memoirs of Binet and Cauchy. Since then 155 other mathematicians contributed 301 publications to the subject, more than three-quarters of which appeared in the last 19 years. The present monograph is an outcome of this remarkable re-awakening of interest in the permanent function.

The purpose of the book is to give a complete account of the theory of permanents, their history and applications, in a form accessible not only to mathematicians but also to workers in various applied fields, and to students of pure and applied mathematics. Here is the first complete account of the theory of permanents. It is a survey in the style of MacDuffy The Theory of Matrices and of A Survey of Matrix Theory and Matrix Inequalities, by Marcus and Minc. However, it differs from both works in several respects: the style is more leisurely, the proportion of theorems proved in the text is higher, and the scope is wider—the volume covers virtually the whole of the subject, a feature that no survey of the theory of matrices can even attempt. Apart from many theorems proved in detail, there are numerous results stated without proof. Due to limitation of space, not every known result could be mentioned in the text. The choice of the theorems included in the book reflects, of course, the author's predilections.