The electric heating system, in particular for a hybrid vehicle or electric vehicle, is provided with a heating module. The heating module is provided with an electrically insulating, heat conducting ceramic substrate which has a heating zone and a control zone which are spaced apart from one another. The heating module comprises an electrical resistance heating element which is arranged on the ceramic substrate, in the heating zone thereof, and which is embodied as a resistance heating conductor which is mounted on the ceramic substrate. Further, the heating module comprises a transistor for controlling the current through the resistance heating conductor, wherein the transistor and other optionally present electrical components and conductor tracks are arranged in the control zone on the ceramic substrate. The heating module is provided with a first cooling element which is thermally coupled to the heating zone of the ceramic substrate.