This book is aimed primarily at undergraduates in mathematics and the physical sciences. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples. The basic topics of vector geometry, differentiation and integration in several variables are explored. It also provides numerous computer algebra illustrations and tutorials using MATLAB or MAPLE. Brief Table of Contents: 1. Geometry in R2. 2. Geometry in R3. 3. Multivariable Functions. 4. Partial Derivatives. 5. Partial Derivatives. 6. Differentiation.7. Taylor'¬"s Theorem and Optimization. 8. Inverse Function Theorem and Implicit Function Theorem. 9. Multiple Integration. 10. Differential Forms and Stokes'¬" Theorem.