Fundamental of Mathematical Analysis -I

This volume presents an expanded and refined exploration of the mathematical analysis of univariate real functions developed from a series of eleven postgraduate lectures on Real Analysis first delivered in September 2016. Building upon the foundations of a previous textbook this extended edition deepens the discussion of core analytical concepts and introduces several new sections-marked with an asterisk (*)-that address advanced topics not covered in the original lectures. Structured into eleven comprehensive chapters and an appendix the book offers a rigorous yet accessible path through the essential tools theorems and techniques of real analysis. It is designed for graduate students instructors and researchers seeking a solid and modern treatment of the subject. Serving both as a standalone reference and a prelude to the forthcoming Mathematical Analysis I⁺ which will further expand the theory with six new chapters and three appendices this work continues the author's pursuit of clarity depth and mathematical precision.