An editor's preface to a mathematics book does not have a clearly defined role in contemporary usage. If some past precedents were followed, I would merely remark that the present work by John Dollard and Charles Friedman is a completely self-contained treatment of the product integral on a simple and elementary basis. As such, I believe it to be unique as far as this topic is concerned. The applications that are presented fall mainly within the domain of ordinary differential equations. Some amplifications of the generality of the theme with applications to a wider circle of mathematical topics are described in the accompanying Appendix by P. R. Masani.

For the benefit of some readers at least, I shall go beyond this conventional restriction of the editor's function. Though in the last analysis, mathematical topics must be treated in full technical detail and with logical completeness (as they are indeed treated in the body of the present work), it is often useful to preface such a detailed development with a more discursive and less technical discussion.

What is the product integral? As the text tells us, it is an analytic process or class of processes first put forward by Volterra in the last decades of the nineteenth century for the study of various questions relating to the theory of ordinary differential equations. As Professor Masani reminds us in his Appendix, it was extensively developed by Schlesinger in the early part of the twentieth century, particularly in connection with differential equations in the complex domain.