A heat exchanger for media-separated heat transfer between a first fluid and a second fluid, - comprising a heat exchanger block having a block longitudinal direction, a block transverse direction and a block height direction which are perpendicular to each other, - wherein the heat exchanger block has two block longitudinal ends facing away from each other in the block longitudinal direction and two block transverse ends facing away from each other in the block transverse direction, - wherein the heat exchanger block has a plurality of tubes through which the first fluid can flow, which tubes extend parallel to the block longitudinal direction and are arranged next to one another in the block transverse direction, - wherein a plurality of interstices through which the second fluid can flow are formed on the heat exchanger block, which interstices are each located between two tubes which are adjacent in the block transverse direction and which pass through the heat exchanger block in the block height direction, - wherein the heat exchanger block has at each of its longitudinal block ends a head shell which extend parallel to the block transverse direction, are penetrated by the tubes, are soldered to the tubes and each have two shell transverse ends facing away from one another in the block transverse direction, - wherein the heat exchanger block has a cover plate at each of its block transverse ends, which extend parallel to the block longitudinal direction, are soldered to the head shells and each have two plate longitudinal ends facing away from one another in the block longitudinal direction, - wherein the heat exchanger block has four anchorages, each of which connects one of the longitudinal plate ends directly to one of the transverse shell ends in a form-fitting manner, - wherein the respective anchorage has a lug extending in the block longitudinal direction and having a hook projecting from the lug in the block transverse direction, and a hook opening open in the block transverse direction and having an opening edge bounding the hook opening in the block longitudinal direction, - wherein the hook engages in the hook opening in the block transverse direction and is supported on the opening edge in the block longitudinal direction, characterized in - that the hook has a hook end which is supported on the opening edge via a linear or point contact zone or via a plurality of linear or point contact zones. - comprising a heat exchanger block having a block longitudinal direction, a block transverse direction and a block height direction which are perpendicular to each other, - wherein the heat exchanger block has two block longitudinal ends facing away from each other in the block longitudinal direction and two block transverse ends facing away from each other in the block transverse direction, - wherein the heat exchanger block has a plurality of tubes through which the first fluid can flow, which tubes extend parallel to the block longitudinal direction and are arranged next to one another in the block transverse direction, - wherein a plurality of interstices through which the second fluid can flow are formed on the heat exchanger block, which interstices are each located between two tubes which are adjacent in the block transverse direction and which pass through the heat exchanger block in the block height direction, - wherein the heat exchanger block has at each of its longitudinal block ends a head shell which extend parallel to the block transverse direction, are penetrated by the tubes, are soldered to the tubes and each have two shell transverse ends facing away from one another in the block transverse direction, - wherein the heat exchanger block has a cover plate at each of its block transverse ends, which extend parallel to the block longitudinal direction, are soldered to the head shells and each have two plate longitudinal ends facing away from one another in the block longitudinal direction, - wherein the heat exchanger block has four anchorages, each of which connects one of the longitudinal plate ends directly to one of the transverse shell ends in a form-fitting manner, - wherein the respective anchorage has a lug extending in the block longitudinal direction and having a hook projecting from the lug in the block transverse direction, and a hook opening open in the block transverse direction and having an opening edge bounding the hook opening in the block longitudinal direction, - wherein the hook engages in the hook opening in the block transverse direction and is supported on the opening edge in the block longitudinal direction, characterized in - that the hook has a hook end which is supported on the opening edge via a linear or point contact zone or via a plurality of linear or point contact zones.