Nonstandard analysis represents a fundamental change of perspective in mathematics (and sciences), comparable to the introduction of Cantor's set theory in the nineteenth century. This book is a short, readable introduction to the subject, based on the axiomatic or IST approach. The first part gives a clear, rigorous exposition of the theory; the second part consists of a number of self-contained chapters dealing with applications. As an aid to self-study, the author has included exercises at the end of each chapter, with hints as well as full solutions. This book will be invaluable for students, teachers and researchers wishing to learn about nonstandard analysis, either for its applications to other branches of mathematics and science, or for its own sake.