This textbook is prepared to serve as an updated companion to the students studying mathematics in the undergraduate major and minor courses of studies as introduced in NEP. The book comprises of twelve chapters which are considered in three basic units. The first unit considers Calculus which, in six chapters, discusses thoroughly the criterion of differentiability of functions, higher order derivatives, indeterminate forms, integration by successive reductions and certain applications of integral calculus which enable one to determine the length of a plane curve, area enclosed by plane curves, volume and surface of revolutions of a region enclosed by plane curves. The second unit considers Geometry which, in four chapters, analyses a depth discussions on the basic concepts of conics under the Cartesian and Polar system of co-ordinates, Quadric surfaces (Conicoids) and Generating lines. Finally the third unit considers Vector Analysis which, in its two chapters, discusses thoroughly the complete concept of vector with certain of its applications in algebra and geometry, differentiation and integration of vector functions of single variable. Each chapter is designed with sufficient number of worked-out examples and exercise for the practice purpose of the students. However the book is sure to be an excellent companion to all aspiring students studying mathematics in the undergraduate level of studies in any university of India.