''Transversal theory, the study of combinatorial questions of which Philip Hall's classical theorem on 'distinct representatives' is the fount and origin, has only recently emerged as a coherent body of knowledge. The pages that follow represent a first attempt to provide a codification of this new subject and, in particular, to place it firmly in the context of the theory of abstract independence. I have sought to make the exposition leisurely, systematic, and as nearly self-contained as possible; but since the length of the book had to be kept within conventional bounds, it has been necessary to exclude certain topics even though they impinge on my central theme. Thus I say nothing about the subject of 'flows in networks' initiated by Ford and Fulkerson; I pass in silence over the exciting possibilities of establishing combinatorial theorems by the method of linear programming; and I refer only occasionally to the theory of graphs. I hope that as a result my presentation has gained in care and clarity what it has undoubtedly lost in breadth of treatment.The account offered here is intended primarily for three classes of readers. It aims to serve as a detailed introduction to the methods of transversal theory for postgraduate students who wish to specialize in combinatorial mathematics. It will, perhaps, provide a convenient work of reference for experts in the field. And finally, it is a repository of combinatorial results which those engaged in the application of mathematical techniques to practical problems may find occasion to invoke...'' L.Mirsky