One of the purposes of this thesis is to study the gravitomagnetic effects. These effects are derived by the analogy between Coulomb?s law and Newton?s gravitation law. There is a relationship between Maxwell?s equations and the linearized Einstein equations. Therefore, our rst step will be to linearize the Einstein field equations and compare them with some electromagnetic phenomena. Then, we will take the MPD equations given by Plyastsko et al. for a spinning test particle orbiting around a rotating massive body. Since it is not possible to nd an analytical solution for the set of eleven coupled differential equations, we will give a numerical solution for the case when the spinning test particle orbits in a Kerr metric. The main contribution of this work is to yield the numerical solution for the case of spinning particles around a rotating gravitational eld. On the other hand, one nds that the majority of works give the analytical solution for particular cases such as spinless test particles in the Schwarzschild metric and in the equatorial planes or the spin values constricted in the time. We calculate the trajectories of spinning test particles in rotating gravitational elds without restrictions on its velocity and spin orientation. From this work, we will study the gravitomagnetism effects and give an exact numerical solution for the clock effect.