ASMA OSMAN OMER ALI2018-10-102018-10-102008http://hdl.handle.net/123456789/13145A Thesis Submitted in a fulfillment for Ph.D. Degree _ In MathematicsTHE 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.enAPPROACH MECHANICSThesis