Real analysis is a branch of mathematics that focuses on the theory and properties of real numbers. It involves the study of limits, continuity, differentiation, integration, sequences, and series of real-valued functions. Real analysis provides the foundation for many areas of mathematics, including calculus, probability theory, and functional analysis. It is a fundamental subject for anyone interested in studying advanced mathematics or pursuing a career in fields such as engineering, physics, or economics. In this book, the principles and techniques of real analysis are presented in a clear and rigorous manner, with numerous examples and exercises to aid understanding and practice.