As its title indicates, this book is intended to serve as a textbook for an introductory course in mathematical analysis. In preliminary form the book has been used in this way at the University of Michigan, Indiana University, and Texas A&M University, and has proved serviceable. In addition to its primary purpose as a textbook for a formal course, however, it is the authors' hope that this book will also prove of value to readers interested in studying mathematical analysis on their own. Indeed, we believe the wealth and variety of examples and exercises will be especially conducive to this end. A word on prerequisites. With what mathematical background might a prospective reader hope to profit from the study of this book? Our conscious intent in writing it was to address the needs of a beginning graduate student in mathematics, or, to put matters slightly differently, a student who has completed an undergraduate program with a mathematics major. On the other hand, the book is very largely self-contained and should therefore be accessible to a lower classman whose interest in mathematical analysis has already been awakened.