THE ABSTRACT
The problem of quantizing gravity is a longstanding problem. Many
approaches are accomplished to solve this problem. The Feynman
path integral approach and Twistor program are just two trials. In our
thesis we discussed both of them. However the geometrical
quantization approach seems more promising. For this reason we built
our construction of geometrical quantization of mechanics on any
curved space, not necessarily Minkowskian. The geometric
quantization passes through several steps that have been studied in our
thesis.
