Using a progressive but flexible format, this text develops the principles of real analysis and shows how they can be used in a wide variety of applications. The theory and principles of real analysis are treated thoroughly, including basic and advanced examples. The applications form more than half of the book. Each is developed in its own chapter, and they show the wide range of classical and modern subjects in which real analysis is used. Building on students' knowledge of calculus and linear algebra, this text prepares them both for more intensive study of each application and for more advanced work in analysis.