The present book aims at providing a detailed account of the basic concepts of vectors that are needed to build a strong foundation for a student pursuing career in mathematics. These concepts includeâ "Addition and Multiplication of vectors by Scalars, Centroid, Vector Equations of a Line and a Plane and their application in Geometry and Mechanics, Scalar and Vector product of two vectors, Differential and Integration of vectors, Differential Operators, Line Integrals, and Gaussâ s and Stokeâ s Theorems. It is primarily designed for B.Sc and B.A. Courses, elucidating all the fundamental concepts in a manner that leaves no scope for illusion or confusion. The numerous high-graded solved examples provided in the book have been mainly taken from the authoritative textbooks and question papers of various university and competitive examinations which will facilitate easy understanding of the various skills necessary in solving the problems. In addition, these examples will acquaint the readers with the type of questions usually set at the examinations. Furthermore, practice exercises of multiple varieties have also been given, believing that they will help in quick revision and in gaining confidence in the understanding of the subject. Answers to these questions have been verified thoroughly. It is hoped that a thorough study of this book would enable the students of Mathematics to secure high marks in the examinations.