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1 Why quantum gravity? 1
2 Covariant approaches to quantum gravity 23
3 Parametrized and relational systems 61
4 Hamiltonian formulation of general relativity 85
5 Quantum geometrodynamics 118
6 Quantum gravity with connections and loops 165
7 Quantization of black holes 179
8 Quantum cosmology 208
9 String theory 235
10 Quantum gravity and the interpretation of quantum theory 262

The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction - the direct quantization of Einstein's general theory of relativity and string theory - are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centers around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantization of black holes, quantum cosmology, the indications of a discrete structure of spacetime, and the origin of irreversibility. This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science.