Khalid Masoud Makin Mohamed Ali2018-09-202018-09-202007http://hdl.handle.net/123456789/12784A Thesis Submitted in a Fulfillment for PhD. Degree ln MathematicsABSTRACT We considered the problem of geometric quantization. We first started with the classical symplectic geometry and then'we used the complex line bundle to describe prequantization and quantization. Geometrically the Hilbert space of quantum states is constructed from the sections of the complex line bundle over the phase space. We then used the invariance group approach to the geometric quantization.enPHYSICAL FIELDSThesis