This text is intended for a one-semester course in the Calculus of functions of several variables and vector analysis taught at college level. This course is, normally known as, vector calculus, or multi variable calculus, or simply calculus-III. The course usually is preceded by a beginning course in linear algebra. The prerequisite for this course is the knowledge of the fundamental of one-variable calculus, differentiation and integration of the standard functions. The text includes most of the basic theories as well as many related examples and problems. There are many exercises throughout the text, which in my experience are more than enough for a semester course in this subject. I include enough examples for each topics in each section to illustrate and help the student to practice his/her skills. Also, added problems that ask the student to reflect on and explore in his/her own words some of the important ideas of Vector Calculus. I have included material enough to be covered during a simple semester with-out a hassle, and it should be possible to work through the entire book with reasonable care. Most of the exercises are relatively routine computations to moderate and productive problems, to help the students understand the concept of each topic. Each section in a chapter is concluded with a set of exercises that review and extend the ideas that was introduced in the chapter, or section. Computer softwares were not included in this book. Most of the exercises can be solved easily by hand, but I advise the students to use Mathematica, or Maple to graph the functions in each problem to visualize the problem, and understand it better. Some of the homework might require the use of Mathematica.