This textbook offers a high level introduction to multi variable differential calculus Differential forms are introduced incrementally in the narrative eventually leading to a unified treatment of Green s Stokes and Gauss theorems Furthermore the presentation offers a natural route to differential geometry Contents Calculus of Vector FunctionsTangent Spaces and 1 formsLine IntegralsDifferential Calculus of MappingsApplications of Differential CalculusDouble and Triple IntegralsWedge Products and Exterior DerivativesIntegration of FormsStokes Theorem and Applications Numerous figures allow for easy to grasp explanations of the mathematical concepts Differential forms are used throughout the book to motivate vector calculus Includes the necessary material from linear algebra set theory basic topology