The growing interest in missions to the moons of Jupiter and Saturn motivates trajectory optimization within these systems. This thesis focuses on the computation of propellant mass optimal trajectories for spacecraft with low thrust propulsive systems in the Saturn-Titan system. The Circular Restricted Three Body Problem (CR3BP) is used to describe the dynamical environment. The equations are modified to incorporate low thrust contributions. The method to generate an initial guess trajectory is defined. Trajectory optimization using primer vector theory is used along with multiple shooting to generate the required transfers. Necessary conditions are derived for the chosen dynamical system. Propellant mass optimal transfers to vertical and halo target orbits are computed to achieve coverage of the polar regions of Titan. The resultant halo orbit transfer is then utilized to generate transfers to a nearby NRHO orbit for closer approaches to the south polar region.