An exhaust-gas cooler for a motor vehicle is provided that includes a flow path which can be traversed by exhaust gas of an internal combustion engine and which has an inlet region and an outlet region for the exhaust gas, a housing which surrounds the flow path and which has at least one inlet and at least one outlet for a liquid coolant of a coolant circuit, wherein the coolant can flow around the flow path in order to cool the exhaust gas, and wherein the coolant circuit is formed as a main cooling circuit of the internal combustion engine of the motor vehicle, wherein the exhaust-gas cooler is arranged in the main cooling circuit in series with the internal combustion engine.