Canonical Gravity: From Classical to Quantum

These lectures are meant as an introduction to an area of quantum gravity which is still close to the original ideas of classical relativity and which has seen significant progress recently. It is also a thorough introduction to the canonical formalism which will make the subject accessible also to non-specialists and especially to graduate students.

Prima facie questions in quantum gravity.- Hamilton's formalism for systems with constraints.- The classical theory of canonical general relativity.- Ashtekar variables in classical general relativity.- Quantization of systems with constraints.- Canonical quantum gravity and the question of time.- The semiclassical approximation to quantum gravity.- Loop representations.- Gauge theory and gravity in the loop formulation.- Reduced models for quantum gravity.- Adjointness relations as a criterion for choosing an inner product.- Overview and outlook.