Abstract: An air conditioning system for an air-conditioning of spaces comprises a compressor for compressing a refrigerant in a refrigerant circuit, a first heat exchanger for exchanging heat between the refrigerant and a heat reservoir, a plurality of throttles for expanding the refrigerant, a plurality of second heat exchangers for exchanging heat between the refrigerant and a heat transfer fluid in one associated heat transfer fluid circuit each, and a plurality of third heat exchangers which each are arranged in an associated space, for exchanging heat between the heat transfer fluid and indoor air of the associated space. To a second heat exchanger a throttle and a heat transfer fluid circuit with a plurality of third heat exchangers are associated.