Some Professors of Mathematics like to present the multivariable calculus, by presenting only the theory. Herein we explain the theory of multivariable calculus by exposing the theory with clear examples. We end this book with three chapters about double and triple integration with clear examples and a lot of solved problems with clear figures for exposing the methods of integration. This book is a second version of the previous published book with the same title: "Multivariable Calculus, Theory and Exercises".