This textbook has been designed to meet the needs of B.Sc. First Semester students of Mathematics as per Common Minimum Syllabus prescribed for Ranchi University and other Universities and Colleges under the recommended National Education Policy 2020 in Jharkhand. To possess an in-depth knowledge of the subjects, topics such as Differentiability of a Function, Chain Rule of Differentiation, Mean Value Theorems, Darboux Theorem, Successive Differentiation: Leibniz's Theorem, Maclaurin and Taylor's Theorems, Curvature, Asymptotes and Curve Tracing, Integration of Rational and Irrational Functions, Definite and Special Integrals, Reduction Formulae, Length and Area Bounded by Plane Curves, Volume and Surface Area of Solid of Revolution, Planes, Straight Lines and Spheres etc. are well explained.