Lift and slide parking systems employ a plurality of novel trolley apparatus. Each trolley includes a rectangular frame from which a platform may be raised and lowered via cables coupled to lifting bars positioned at each of four corners of the platform. On one side of the frame a slide rail and trolley sliding assembly includes hydraulic cylinders coupled with cables routed through sheaves arranged to enable movement of the trolley horizontally a necessary distance. The slide rail may include grooves in which a sliding block may be slidably retained. On the side opposite the slide rail is a lift rail and platform lift assembly which includes a hydraulic cylinder coupled with one or more belts routed through rollers to a lifting block coupled with cables routed through sheaves and coupled to lifting bars arranged to enable vertical movement of the platform. The lift rail may include grooves in which a cylinder block and lift block are slidably retained. A sliding roller at each corner of the frame is positioned to engage in tracks attached to the superstructure which run the width of the parking system.