Basic Analysis I: Functions of a Real Variable is designed for students who have completed the usual calculus and ODE sequence and a basic course in linear algebra. This is a critical course in the use of abstraction. "Mathematics is fortunate to be populated by bright practitioners. Nonetheless, amongst these we are fortunate to have rare individuals who are wise. Professor Peterson is a member of this distinguished group. His works clearly demonstrate the importance of a long career of research and teaching where he combines the two perspectives of: (1) clearly understanding the needs of diverse readers for clear exposition that scaffolds their exposure to complex material with a transparency about both where they are going and what the utility is of what they are currently reading; and, (2) the benefits of having used the mathematics under consideration in so many diverse applications. The masterly synthesis of so much complex material by a single individual is a superb achievement which will reward serious readers with insight, surprise, and breadth as well as depth."- Professor John R. Jungck, University of Delaware "Analysis is the bedrock of rigorous mathematical thinking and abstraction. Prof. Peterson's book does a fascinating job by taking a critical approach - highly recommended." - Professor Nithin Nagaraj, National Institute of Advanced Studies "Dr. Peterson's thoughtful and detailed explanations?reflect his insights to a very fundamental but complex subject in Mathematics. The treatment in the book does justice to recent trends in Mathematical Analysis while staying true to the classical spirit of the subject. A thoroughly enjoyable read." - Professor Snehanshu Saha, BITS PIlani (K K Birla Goa Campus)