Biomass heating system for burning fuel in the form of pellets and/or wood chips, having: a boiler with a combustion device; a heat exchanger with an inlet and an outlet; wherein the combustion device possesses a combustion chamber with a primary combustion zone and with a secondary combustion zone arranged downstream of it; wherein the secondary combustion zone of the combustion chamber is fluidly connected with the inlet of the heat exchanger; wherein the primary combustion zone is laterally enclosed by a plurality of combustion chamber bricks, characterised in that the biomass heating system is further provided with a flue gas condenser that is provided downstream of the heat exchanger and fluidly connected to this; wherein: the flue gas condenser possesses a first fluid connection and a second fluid connection for supplying a heat exchange medium to the flue gas condenser; and the flue gas condenser possesses a plurality of U-shaped heat exchange pipes, wherein the plurality of U-shaped heat exchange pipes is arranged in groups in a first direction parallel to one another; and wherein a number of the U-shaped heat exchange pipes is connected fluidly in parallel, so as to form a group of heat exchange pipes; wherein the groups of heat exchange pipes are arranged in a second direction parallel to one another; wherein the groups of heat exchange pipes are fluidly connected in series together between the first fluid connection and the second fluid connection; the plurality of U-shaped heat exchange pipes is arranged such that they form a cross counter flow configuration in relation to the flow through the plurality of heat exchange pipes with the flue gas. a boiler with a combustion device; a heat exchanger with an inlet and an outlet; wherein the combustion device possesses a combustion chamber with a primary combustion zone and with a secondary combustion zone arranged downstream of it; wherein the secondary combustion zone of the combustion chamber is fluidly connected with the inlet of the heat exchanger; wherein the primary combustion zone is laterally enclosed by a plurality of combustion chamber bricks, characterised in that the biomass heating system is further provided with a flue gas condenser that is provided downstream of the heat exchanger and fluidly connected to this; wherein: the flue gas condenser possesses a first fluid connection and a second fluid connection for supplying a heat exchange medium to the flue gas condenser; and the flue gas condenser possesses a plurality of U-shaped heat exchange pipes, wherein the plurality of U-shaped heat exchange pipes is arranged in groups in a first direction parallel to one another; and wherein a number of the U-shaped heat exchange pipes is connected fluidly in parallel, so as to form a group of heat exchange pipes; wherein the groups of heat exchange pipes are arranged in a second direction parallel to one another; wherein the groups of heat exchange pipes are fluidly connected in series together between the first fluid connection and the second fluid connection; the plurality of U-shaped heat exchange pipes is arranged such that they form a cross counter flow configuration in relation to the flow through the plurality of heat exchange pipes with the flue gas. the flue gas condenser possesses a first fluid connection and a second fluid connection for supplying a heat exchange medium to the flue gas condenser; and the flue gas condenser possesses a plurality of U-shaped heat exchange pipes, wherein the plurality of U-shaped heat exchange pipes is arranged in groups in a first direction parallel to one another; and wherein a number of the U-shaped heat exchange pipes is connected fluidly in parallel, so as to form a group of heat exchange pipes; wherein the groups of heat exchange pipes are arranged in a second direction parallel to one another; wherein the groups of heat exchange pipes are fluidly connected in series together between the first fluid connection and the second fluid connection; the plurality of U-shaped heat exchange pipes is arranged such that they form a cross counter flow configuration in relation to the flow through the plurality of heat exchange pipes with the flue gas.