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This book aims to present a pedagogical and self-consistent
treatment of the canonical approach to Quantum Gravity, starting
from its original formulation to the most recent developments in
the field.We start with an innovative and enlightening introduction
to the formalism and concepts on which General Relativity has been
built, giving all the information necessary in the later analysis.
A brief sketch of the Standard Cosmological Model describing the
Universe evolution is also given alongside the analysis of the
inflationary mechanism. After deepening the fundamental properties
of constrained dynamic systems, the Lagrangian approach to the
Einsteinian Theory is presented in some detail, underlining the
parallelism with non-Abelian gauge theories. Then, the basic
concepts of the canonical approach to Quantum Mechanics are
provided, focusing on all those formulations which are relevant for
the Canonical Quantum Gravity problem. The Hamiltonian formulation
of General Relativity and its constrained structure is then
analyzed by comparing different formulations. The resulting quantum
dynamics, described by the Wheeler-DeWitt equation, is fully
discussed in order to outline its merits and limits. Afterwards,
the reformulation of Canonical Quantum Gravity in terms of the
Ashtekar-Barbero-Immirzi variables is faced by a detailed
discussion of the resulting Loop Quantum Gravity Theory. Finally,
we provide a consistent picture of canonical Quantum Cosmology by
facing the main features of the Wheeler-DeWitt equation for the
homogeneous Bianchi models and then by a detailed treatment of Loop
Quantum Cosmology, including very recent developments.
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