  This article makes no claim to originality, other than, perhaps, the simple
statement here called the {\it Abstract Maximum Principle}. Actually, the whole
contents are strongly based on some H. Sussmann's and coauthors' papers, in
which, in a much more general context, the set-separation approach is regarded
as foundational for necessary conditions for minima. So, rather than being the
exposition of original material, this paper has mainly a pedagogical purpose.
From the Abstract Maximum Principle it is possible to deduce several necessary
conditions for both finite dimensional minimum problems and for optimal control
problems. More in general, this Principle seems apt to capture some
consequences of the geometric and topological idea of (possibly vector-valued)
minimization in a parametrized problem.
