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This textbook offers a comprehensive presentation of undergraduate real analysis for one and several variables, accessible to students with a solid calculus background and some proof experience. It occupies a middle ground in difficulty between basic analysis texts and more advanced courses set in abstract metric spaces. The republication of this book, after nearly 50 years, serves as an excellent resource for course texts or self-study in undergraduate analysis. The book covers essential topics such as number systems, functions, limits, continuity, differentiation, integration, metric spaces, basic point set topology, and more. Unique to this text are the starred sections and exercises that delve into concepts often overlooked in standard courses, including point set topology and Riemann-Stieltjes integration. An innovative opening chapter provides a detailed axiomatic description of number systems, complemented by substantial exercises. The text’s midway difficulty level addresses the current weaknesses in calculus courses, allowing it to serve as a bridge between basic real variables and more rigorous analysis. This means students can rely on one comprehensive, affordable text rather than needing two. Additionally, pragmatic sections cater to applied mathematics, physics, and engineering students. Overall, this versatile textbook is a valuable addition to undergraduate analysis literature, beneficial for both students and