This chapter presents the quantization of canonical gravity in the metric formulation. The central equations are the Wheeler-DeWitt equation and the quantum diffeomorphism constraints, whose general properties are discussed at length. Special attention is focused on conceptual problems such as the problems of time and the inner product. The chapter includes general remarks on the functional Schr\"odinger picture, the connection with path integrals, and the extension of the formalism to quantum supergravity. A detailed section is devoted to the semiclassical approximation. Starting from quantum mechanical analogies, an approximate functional Schr\"odinger equation as well as quantum gravitational corrections are derived and discussed. Possible observational tests are pointed out.
Keywords: Quantum geometrodynamics, Wheeler-DeWitt equation, diffeomorphism constraints, problem of time, inner product, functional Schr\"odinger picture, supergravity, semiclassical approximation, observations
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