With a "less is more" approach to building upon the complete foundations of calculus, this sequence of 6 books introduces the reader to the topics commonly found in a 2nd or 3rd semester/or 2nd- or 3rd-year level of college-level calculus. They introduce the concept of vectors and multiple differentiation and integration, including functions of multiple variables. Examples of applications to physics and other disciplines are offered to illustrate the utility of these advanced calculus tools. This third volume discusses various versions of the chain rule for functions of several variables, showing that while not as useful as using the chain rule for functions of a single variable they can be interpreted in ways that lead to useful general results.