Comprehensive Introduction: Provides a thorough foundation in the fundamental concepts of real analysis, including limits, continuity, differentiation, and integration. Rigorous and Accessible: Presents complex mathematical concepts in a clear and approachable manner, making it suitable for both undergraduate and graduate students. Updated and Expanded: Includes new material on topics such as the Riemann-Stieltjes integral and the Stone-Weierstrass theorem, ensuring up-to-date coverage. Numerous Examples and Exercises: Features a wealth of worked-out examples and practice exercises to reinforce understanding and develop problem-solving skills.* Historical Context: Explores the historical development of analysis, providing insights into the evolution of mathematical ideas.