This book is aimed primarily at higher level undergraduates in the mathematical sciences. Many courses on calculus aim at providing a limited technical skill that is soon forgotten. This book provides a deeper understanding of the subject which will pay dividends in enabling the reader to appreciate the uses and limitations of the techniques of multivariate calculus when he or she applies these to new problems. Sean Dineen has provided a solid description of the basic concepts, via simple familiar explanations which are then tested in technically demanding examples. By recognising the varied background that students can bring to the subject at this level, the author has assumed the minimal amount of prerequisite knowledge necessary to understand the comprehensive view of Differential Calculus, Integral Calculus and the Geometric Calculus of Several Variables which is given in this book.