In Chap.  1 the basic topological notions for the Analysis in Euclidean space were introduced. The richness of the possible domains of functions of several variables has been illustrated and it should be clear that already in dimension \(n=2\) real valued functions may exhibit a variety of behaviours that functions of a single variable do not display. Graphs of functions of two variables may be visualized as surfaces, or, with a bit of informality, as less regular “landscapes”. A very crucial notion for such functions, as it was in the case of a single variable, is the notion of continuity, which appeals to the visual picture that one can “walk along the graph’ in order to reach a given point on it, or one cannot, the hyke is doable or not, the surface breaks or does not break at that point.