The study of Analysis is indispensable for a prospective post graduate students of pure and applied mathematics. Mathematics has become valuable in many areas, including economics, management science as well as the physics, electrodynamics, engeneering and computer science etc. Results and proofs are given at a medium level of generality. This book Analysis contains the concepts of Riemann-Stieltjes integral, Fourier Series, Transcendental functions, Functions of several variables.