Vector is a major tools of Mathematical Physics and also of Mathematics. It is basically a tensor of rank 1 and It has maximum 3 rectangular components. In this course, discussion on Vector and Its properties is made in both basic and advance level with a number of numerical problem solving. At the basic level Vector addition, subtraction along with its component and resolution are discussed where as in advance level, Vector operators and their application with several Vector identities and also Vector line, surface and volume integration are discussed also with a number of numerical solving. The students of both Physics and Mathematics will be highly benefited with this course.