Through four editions this popular textbook attracted a loyal readership and widespread use. Students find the book to be concise, accessible, and complete. Instructors find the book to be clear, authoritative, and dependable. The primary goal of this new edition remains the same as in previous editions.It is to make real analysis relevant and accessible to a broad audience of students with diverse backgrounds while also maintaining the integrity of the course. This text aims to be the generational touchstone for the subject and the go-to text for developing young scientists.This new edition continues the effort to make the book accessible to a broader audience. Many students who take a real analysis course do not have the ideal background. The new edition offers chapters on background material like set theory, logic, and methods of proof.The more advanced material in the book is made more apparent.This new edition offers a new chapter on metric spaces and their applications. Metric sp