The aim of this work is to analyze the feasibility of Earth-Moon transfers using weak stability boundary, in order to reach a Halo orbit around L2. The analysis is firstly conducted in the CR3BP (Circular Restricted 3 Body Problem) and afterwards perturbations are introduced. The objective of such transfer is to reduce the mission cost by lowering the propellant requirements compared to a traditional Hohmann transfer, aiming for a ballistic capture at Moon arrival. Such capture is possible using region in space in which the gravitation forces of the influencing bodies tend to balance each other, called weak stability boundary. Firstly a suitable destination Halo orbit is computed using differential correction in a single shooting method, with an attention to the stability of the Halo orbit in order to reduce station keeping costs.