Abstract
In this thesis, we will discuss the propagation of a Dirac particle in the gravitational field, and exploring its gyrogravitational ratio and other effects. We use the coordinate transformations to study a scalar particle's Lense-Thirring effect, then searching for the transformation operator from an inertial frame to an moving accelerated frame in order to find the gyrogravitational ratio of a spin 1/2 particle. Afterwards, we solve the Dirac wave function in a uniformly gravitational field for the sake of studying its change of polarization and compare it with the effects of a macroscopic object in the same gravitational field.