Exhaust gas cooler for an exhaust gas system or to an exhaust gas recirculation system of an internal combustion engine, - having an exhaust gas path which leads from an exhaust gas inlet to an exhaust gas outlet, - and having a coolant path, which is coupled in a heat-transferring manner to the exhaust gas path, - wherein the exhaust gas path has an inlet region, which comprises the exhaust gas inlet and which is configured for an inlet cooling power, - wherein, downstream of the inlet region, the exhaust gas path has an intermediate region which is configured for an intermediate cooling power, which is less than the inlet cooling power, - wherein, downstream of the intermediate region, the exhaust gas path has an outlet region, which comprises an exhaust gas outlet which is configured for an outlet cooling power which is greater than the intermediate cooling power, characterised in that - the exhaust gas cooler is designed as a finned-tube heat exchanger, in which a plurality of coolant tubes extend through the exhaust gas path, which conduct the coolant inside and which bear fins outside, at least in the inlet region and in the outlet region, - the coolant path has an inlet chamber, a plurality of deflection chambers (24, 25, 26, 27) and an outlet chamber, which are connected together fluidically in series via groups (29, 30, 31, 32, 33) of coolant tubes which are led through the exhaust gas path, - the inlet chamber comprises a coolant inlet and is fluidically connected to one of the deflection chambers (24, 25, 26, 27), - the deflection chambers (24, 25, 26, 27) are fluidically connected with one another, - and the outlet chamber comprises a coolant outlet and is fluidically connected to another of the deflection chambers (24, 25, 26, 27). - having an exhaust gas path which leads from an exhaust gas inlet to an exhaust gas outlet, - and having a coolant path, which is coupled in a heat-transferring manner to the exhaust gas path, - wherein the exhaust gas path has an inlet region, which comprises the exhaust gas inlet and which is configured for an inlet cooling power, - wherein, downstream of the inlet region, the exhaust gas path has an intermediate region which is configured for an intermediate cooling power, which is less than the inlet cooling power, - wherein, downstream of the intermediate region, the exhaust gas path has an outlet region, which comprises an exhaust gas outlet which is configured for an outlet cooling power which is greater than the intermediate cooling power, characterised in that - the exhaust gas cooler is designed as a finned-tube heat exchanger, in which a plurality of coolant tubes extend through the exhaust gas path, which conduct the coolant inside and which bear fins outside, at least in the inlet region and in the outlet region, - the coolant path has an inlet chamber, a plurality of deflection chambers (24, 25, 26, 27) and an outlet chamber, which are connected together fluidically in series via groups (29, 30, 31, 32, 33) of coolant tubes which are led through the exhaust gas path, - the inlet chamber comprises a coolant inlet and is fluidically connected to one of the deflection chambers (24, 25, 26, 27), - the deflection chambers (24, 25, 26, 27) are fluidically connected with one another, - and the outlet chamber comprises a coolant outlet and is fluidically connected to another of the deflection chambers (24, 25, 26, 27).