In a piston pump (1) having a differential piston (12) positioned in a cylindrical housing (11) and translationally drivable, a first pressure chamber (13) of the differential piston (12) is connectable to a second pressure chamber (14) via a check valve (16) inserted into a connecting line (15), and to a storage reservoir (2) via an inlet valve (23). The differential piston (12) is provided with a dipping piston (41) attached to a piston rod (31). In addition, a pass-through (32) of the piston rod (31) from the first pressure chamber (13) is closed fluid-tight by seals (34), and a transport line (22) is positioned laterally offset from or concentric to the piston rod (31) in the vicinity of the pass-through (32) of the latter.