This book is based on a course in real analysis offered to advanced undergraduates and first-year graduate students at Bowling Green State University. In many respects it is a perfectly ordinary first course in analysis, but there are some important differences. For one, the typical audience for the class includes many nonspecialists, students of statistics, economics, and education, as well as students of pure and applied mathematics at the undergraduate and graduate levels. What's more, the students come from a wide variety of backgrounds. This makes the course something of a challenge to teach. The material must be presented efficiently, but without sacrificing the less well-prepared student. The course must be essentially self-contained, but not so pedestrian that the more experienced student is bored. And the course should offer something of value to both the specialist and the nonspecialist. The following pages contain my personal answer to this challenge.

To begin, I make a few compromises: Extra details are given on metric and normed linear spaces in place of general topology, and a thorough attack on Riemann–Stieltjes and Lebesgue integration on the line in place of abstract measure and integration. On the other hand, I avoid euphemisms and specialized notation and, instead, attempt to remain faithful to the terminology and notation used in more advanced settings. Next, to make the course more meaningful to the nonspecialist (and more fun for me), I toss in a few historical tidbits along the way.