3-DIMENSIONAL CANONICAL QUANTUM-GRAVITY

General aspects of vielbein representation, ADM formulation and canoni cal quantization of gravity are discussed using pure gravity in three dimensions as a toy model. The classical part focuses on the role of l ocal observers in general relativity, who will Later be identified wit h quantum observers. A precise definition of gauge symmetries and a cl assification of inequivalent solutions of Einstein's equations in the dreibein formalism is given as well. In the quantum part the construct ion of the physical Hilbert space is carried out explicitly for a toru s- and cylinder-type space manifold, which has not been done so far. S ome conceptual problems of quantum gravity are considered from the poi nt of view of an observer sitting inside the universe.