This book is written in accordance with the UGC model syllabus prepared by a team of experts on the initiative of UGC, covers the syllabus of calculus and will serve as a textbook for undergraduate students of Indian Universities. This book may be most useful for engineering students and others preparing for competitive examinations like IAS, IES, PCS etc. The text starts with the concepts of limit, continuity, differentiability and is followed by the study of successive differentiation, tangents and normals, Rolle's theorem, Lagrange's mean value theorem, Taylor's theorem, Taylor's and Maclaurin's series, indeterminate forms, partial differentiation, curvature, asymptotes, concavity, convexity and points of inflexion, singular points, tracing of the curves, elementary integration, integration of rational functions, irrational algebraic functions and trigonometric functions, definite integrals, reduction formulae, quadrature, rectification and volumes and surfaces of revolution. Moreover, three Appendices on Beta and Gamma functions, Maxima and Minima, and Practicals with Mathematica have also been presented.