This thesis is about trajectory optimization by means of an indirect method, based on optimal control theory. Space exploration is constantly increasing and Lagrangian points proved to be strategic locations for either unmanned scientific missions or human outposts thanks to the natural stabilization created by the balance of gravitational and centripetal forces. The study of optimal trajectories from these particular locations is therefore becoming increasingly necessary. A medium-size spacecraft is considered in the present study, whose final objective is to maximize final mass of the spacecraft, thus reducing fuel consumption as much as possible. 4-body gravitational influence with solar radiation pressure as perturbation, is considered in the dynamic model, using JPL ephemeris to track celestial body positions.