This book is intended as a self-study text for students following courses in science and engineering where vectors are used. The material covered and the level of treatment should be sufficient to provide the vector algebra and vector calculus skills required for most honours courses in mechanics, electromagnetism, fluid mechanics, aerodynamics, applied mathematics and mathematical modelling. It is assumed that the student begins with minimal (school-level) skills in algebra, geometry and calculus and has no previous knowledge of vectors. There are brief reviews at appropriate points in the text on elementary mathematical topics: the definition of a function, the derivative of a function, the definite integral and partial differentiation. The text is characterised by short two or three page sections where new concepts, terminologies and skills are introduced, followed by detailed summaries and consolidation in the form of Examples and Problems that test the objectives listed at the beginning of each chapter. Each Example is followed by a fully worked out solution, but the student is well advised to have a go at each Ex. ample before looking at the solution. Many of the Examples and Problems are set in the context of mechanics and electromagnetism but no significant previous knowledge of these subjects is assumed. Bare answers to selected Problems are given at the back of the book. Full solutions to all Problems can be found on www at http://physics. open. ukl-avdurranlvectors. htrnl.