This book is the first of a three volume introduction to analysis. It is distinguished by its modern and clear presentation, concentrating always on the essential concepts. In contrast to most other textbooks, there is no artificial separation between the theories of one variable and that of many variables. Emphasis is placed on the early development of a solid foundation in topology. As well, the basics of complex analysis are covered.

This book is directed primarily to the students and instructors of beginning courses in analysis. But, with the many examples, exercises and the supplementary material, it is also suitable for self-study, as preparation for advanced study, and as a basis for other research in mathematics and physics.

"It is a wonderful book that distinguishes itself by the clarity of presentation, by the fact that it is self-contained and has many exercises at various degrees of difficulty (among many other great qualities.)...[It] is a very elegant and complete treatment of topics usually not found in analysis books...The exercises are plenty and very well selected. In summary, we have here a very-very good, self-contained, well written book, including many applications and exercises, that can be used as a text for courses, as self-study, and/or as a basis for research in mathematics or even other disciplines. This book is a wonderful read." ---MAA Reviews