A master cylinder suitable for a vehicle braking system has an unusual capability to supply quantities of fluid and fluid pressures at its output in differentiated manner in dependence on the braking stage, preventing long transitory stages between an approach stage and an actual braking stage. The cylinder comprises a cylinder body having a first chamber and a second chamber provided inside. The first chamber is in operative communication with at least one braking member and houses a first piston. The second chamber, which has larger transverse dimensions than the first chamber, is in operative communication with the first chamber and houses a second piston. Ducts are provided and put the first chamber and the second chamber into communication during the approach stage. The ducts house a low-pressure valve which is open during the approach stage and closed during the actual braking stage.