This text investigates the fundamental principles of real analysis, focusing on the rigorous construction of the real number system and the properties of functions. Kenneth W. Anderson provides a structured pedagogical approach designed for undergraduate students transitioning from introductory calculus to proof-based mathematics. The book utilizes a logical framework that emphasizes the epsilon-delta definition of limits, continuity, and the convergence of sequences and series to build a comprehensive understanding of analytical concepts.

Mathematics educators often cite this text for its clear, accessible approach to the transition into formal analysis. Readers frequently note the balance between theoretical rigor and the practical clarity required for students encountering proof-based mathematics for the first time.