This book is intended to serve as a text in mathematical analysis for undergraduate and postgraduate students. It opens with a brief outline of the essential properties of rational numbers using Dedekind's cut, and the properties of real numbers are established. This foundation supports the subsequent chapters. The material of some of topics-real sequences and series, continuity, functions of several variables, elementary and implicit functions, Riemann and Riemann-Stieltjes integrals, Lebesgue integrals, line and surface Integrals, double and triple integrals are discussed in details. Uniform convergence, Power series, Fourier series, and Improper integrals have been presented in a simple and lucid manner. A large number of solved examples taken mostly from lecture notes make the book useful for the students. A chapter on Metric Spaces discussing completeness, compactness and connectedness of the spaces and two appendices discussing Beta-Gamma functions and Cantor's theo CONTENTS: Real Numbers Open Sets, Closed Sets and Countable Sets Real Sequences Infinite Series Functions of a Single Variable (I) Functions of a Single Variable (II) Applications of Taylor's Theorem Functions The Riemann Integral The Riemann-Stieltjes Integral Improper Integrals Uniform Convergence Power Series Fourier Series Functions of Several Variables Implicit Functions Integration on R2 Integration on R3 Metric Spaces The Lebesgue Integral ry of real numbers add glory to the contents of the book.