The methods of Abraham Robinson's Nonstandard (or Infinitesimal) Analysis (NSA) are currently being used across the whole spectrum of mathematics – from ‘pure’ mathematics through to mathematical physics. This book is designed as an introduction to NSA and to some of its many applications, with the working mathematician or student particularly in mind. It has emerged from a conference with the same title held at the University of Hull in 1986, which had the aim of making NSA more widely known in the mathematical community through a series of introductory lecture courses and lectures on current research. The first part of this book consists of papers based on the introductory lectures given at the conference by Tom Lindstrøm, Ward Henson, Jerry Keisler and Sergio Albeverio. The latter part of the book contains papers that present a sample of recent developments in the more advanced applications of NSA.

Lindstrøm's An Invitation to Nonstandard Analysis expounds the foundations of the theory. It is designed to be “a friendly welcome requiring no other background than a smattering of general mathematical culture”, offered in the belief that NSA “is of greater interest to the analyst than to the logician”. Lindstrøm writes “I have tried to make the subject look the way it would had it been developed by analysts or topologists and not logicians.” To this end, his presentation of NSA is somewhat different from others in the literature, in that he builds a nonstandard universe and shows how to practice NSA without any use of logic.