When employed with skill and understanding, vector analysis can be a practical and powerful tool. This text develops the algebra and calculus of vectors in a manner useful to physicists and engineers. Numerous exercises (with answers) not only provide practice in manipulation but also help establish students' physical and geometric intuition in regard to vectors and vector concepts. Part I, the basic portion of the text, consists of a thorough treatment of vector algebra and the vector calculus. Part II presents the illustrative matter, demonstrating applications to kinematics, mechanics, and electromagnetic theory. The text stresses geometrical and physical aspects, but it also casts the material in such a way that the logical structure of the subject is made plain. Serious students of mathematics can rigorize the treatment to their own satisfaction. Although intended primarily as a college text, this volume may be used as a reference in vector techniques or as a guide to self-education.