Planar drive system, having a rotor and a stator module, wherein the stator module has a stator module housing, a stator unit for an electric drive of the rotor, and a sensor module for sensing a position of the rotor, wherein the rotor can be driven at least in a first direction and in a second direction via a planar stator surface of the stator unit, wherein the sensor module has a carrier and a two-dimensional arrangement of magnetic field sensors, wherein the magnetic field sensors are arranged on the carrier, characterized in that the two-dimensional arrangement of magnetic field sensors has a first part-arrangement of first magnetic field sensors, in that the first magnetic field sensors of the first part-arrangement are arranged in a first periodic grating, in that the first magnetic field sensors are arranged in the first periodic grating along the first direction and along the second direction, in that adjacent first magnetic field sensors of the first part-arrangement are arranged at a first distance from one another in the first direction, in that adjacent first magnetic field sensors of the first part-arrangement are arranged at a second distance from one another in the second direction, in that the two-dimensional arrangement of magnetic field sensors has a second part-arrangement of second magnetic field sensors, in that the second magnetic field sensors of the second part-arrangement are arranged in a second periodic grating, in that the second magnetic field sensors are arranged in the second periodic grating along the first direction and along the second direction, in that adjacent second magnetic field sensors of the second part-arrangement are arranged at the first distance from one another in the first direction, in that adjacent second magnetic field sensors of the second part-arrangement are arranged at the second distance from one another in the second direction, in that the first part-arrangement and the second part-arrangement are arranged shifted with respect to one another by a vector, in that the vector has a first component in the first direction and a second component in the second direction, in that the first component is smaller than the first distance, in that the second component is smaller than the second distance, in that the rotor has a first magnet unit, in that the first magnet unit has a first periodic arrangement of magnets with a first period length, in that the first periodic arrangement of magnets in the first direction is periodic, in that while the planar drive system is operating the first magnet unit is oriented in the first direction, in that the rotor has a second magnet unit, in that the second magnet unit has a second periodic arrangement of magnets with a second period length, in that the second periodic arrangement of magnets in the second direction is periodic, in that while the planar drive system is operating the second magnet unit is oriented in the second direction, in that the first component is smaller than the first period length, in that a difference between the first distance and the first component is smaller than the first period length, in that the second component is smaller than the second period length, in that a difference between the second distance and the second component is smaller than the second period length, in that the stator unit is arranged on an upper side of the stator module housing, in that the carrier is arranged underneath the stator unit in the stator module housing, in that the carrier has a through-opening, in that the stator module housing has a heat-conducting structure, in that the heat-conducting structure is configured to conduct heat away from the stator unit to an underside, lying opposite the stator surface, of the stator module housing, in that the heat-conducting structure is made to extend from the stator unit through the through-opening to the underside of the stator module housing, in that the through-opening adjoins four magnetic field sensors, and in that in each case two first magnetic field sensors thereof are assigned to the first part-arrangement, and in each case two second magnetic field sensors thereof are assigned to the second part-arrangement.