This is a textbook on several advanced topics. They all have in common that they can be applied in quantum cosmology. The nine chapters of this book are headed as follows: 1. Introduction to general relativity, 2. Elements of cosmology, 3. Constrained Hamiltonian systems, 4. Lagrangian formulations, 5. Quantization methods, 6. Quantum geometrodynamics, 7. Gravity as a gauge theory, 8. Loop quantum gravity, and 9. Quantum cosmology. The 300 items of the reference list give a good overview to the relevant original papers.
The high level of the book can be described as follows: to understand the first chapter “Introduction to general relativity”, the reader should have already read and understood one of the books with title “Introduction to general relativity”.
Publisher’s description: “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.”