If one wishes to express in precise and general terms any statement in physics in which positions, directions and motions in space are involved the most appropriate language to use is the language of vectors. In the mechanics of particles and rigid bodies vectors are used extensively and it is assumed in this monograph that the reader has some prior knowledge of vector algebra, which is the part of vector theory required in mechanics. Nevertheless chapter 1 provides a summary of vector algebra. There the notation to be used is made explicit and a brief survey of the whole field is given with stress laid on a number of particular results that become especially important later. The reader is also given the opportunity to test his understanding of vector algebra and his facility in applying it to detailed problems: a fairly extensive set of examples (exercises A) follows the chapter, with some comments and answers provided at the end of the book.

A considerably widened theory of vectors becomes necessary when one turns to such parts of physics as fluid dynamics and electromagnetic theory where one deals not just with things at certain particular points in space but with the physical objects as distributed continuously in space. Quantities that are continuous functions of the coordinates of a general point in space are called fields and some of the fields of greatest interest in physics are vector fields.