This is a text for a first course in real variables. The subject matter is fundamental for more advanced mathematical work, specifically in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. In addition, many students of engineering, physics, and economics find that they need to know real analysis in order to cope with the professional literature in their fields. Standard mathematical writing, with its emphasis on formalism and abstraction, tends to create barriers to learning and focus on minor technical details at the expense of intuition. On the other hand, a certain amount of abstraction is unavoidable if one is to give a sound and coherent presentation. This book attempts to strike a balance that will reach the widest audience possible without sacrificing precision.