Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields and fluid flow. Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside. This book can be read independently by readers with a basic knowledge in vector algebra. Proofs of all the theorems are developed in detail, with all steps justified. Almost all previously proven results used within proofs and solutions to examples are explicitly cited, and referred to by number. This frustration spent figuring out exactly which results were used and where they were first proved. This book is used for a course at the post-graduate and honours graduate level. It is my hope that the books will also appeal to university students in mathematics. This book has been written to meet the requirement of the students of various universities on this subject which is included in the syllabi of almost all universities. Each topic in this book has been treated in an easy and lucid style without sacrificing any rigidity. The language is simple and easily understandable. This book contain large number of solved examples. At the end of each section, there is a set of exercises.