The purpose of this volume is to present some worked out examples from the theory of Functions in Several Variables in the following topics: 1) Maximum and minimum of a function. 2) Integration in the plane and in the space. 3) Vector analysis. As an experiment I shall here use the following generic diagram for solving problems: A. For Awareness. What is the problem? Try to formulate the problem in your own words, thereby identifying it. D. For Decision. What are we going to do with it? Are there any reasonable solution procedure available? If so, which one should be chosen?.