The right time and place to meet for the first time both the Hessian matrix and the Hessian determinant are about the second year of a course in Mathematical Analysis. However, since this concept is used only once in the whole course, its name is relegated to a footnote or little more. The prescriptions which are given to use the Hessian to conclude whether a critical point of a two-variables function is a maximum or a minimum or a saddle point appear like a mantra, a method which must not satisfy those students who want to know the nature of things. In my attempt to give a general landscape of the mathematical forests where such a carnivorous animal roams, I produced an essay of 34 pages. Don’t be scared: I try to throw light also on other concepts, which generally present many shadowy places. Have courage, and proceed forward.