This textbook is intended for students who wish to obtain an introduction to
the theory of partial differential equations (PDEs, for short), in particular,
those of elliptic type. Thus, it does not offer a comprehensive overview of
the whole field of PDEs, but tries to lead the reader to the most important
methods and central results in the case of elliptic PDEs. The guiding question
is how one can find a solution of such a PDE. Such a solution will, of
course, depend on given constraints and, in turn, if the constraints are of
the appropriate type, be uniquely determined by them. We shall pursue a
number of strategies for finding a solution of a PDE; they can be informally
characterized as follows