  The aim of this review is to provide a detailed account of the physical
content emerging from this story of the canonical approach to Quantum Gravity.
All the crucial steps in our presentation have a pedagogical character,
providing the reader with the necessary tools to become involved in the field.
Such a pedagogical aspect is then balanced and completed by subtle discussions
on specific topics which we regard as relevant for the physical insight they
outline on the treated questions. Our analysis is not aimed at convincing the
reader about a pre-constituted point of view, bu instead our principal goal is
to review the picture of Canonical Quantum Gravity on the basis of the concrete
facts at the ground of its clear successes, but also of its striking
shortcomings.
