Vector analysis is a branch of mathematics that deals with quantities that have both magnitude and direction. The basic objects in vector calculus are scalar fields and vector fields. Recall that a plane is a flat surface that goes on forever in both directions. If we were to place a point on the plane, coordinate geometry gives us a way to describe exactly where it is by using two numbers. A coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space. The term coordination geometry is used in a number of related fields of chemistry and solid state chemistry/physics. When employed with skill and understanding, vector analysis can be a practical and powerful tool. Though, written to meet the requirements of graduate students, it can will also be useful to physicists and engineers.