In this introduction to real analysis, a branch of mathematical analysis dealing with the set of real numbers and their operations, Paul Zorn (St. Olaf College) aims to develop ideas already familiar from elementary calculus in a rigorous manner. The text will help students deeply understand some basic but crucial mathematical ideas, and to see how definitions, proofs, examples, and other forms of the mathematical ?apparatus? work together to create a unified theory. A key feature of the book is that it includes substantial treatment of some foundational material, including general theory of functions, sets, cardinality, and basic proof techniques.