Proposed herein is a burner (20) for the combustion of hydrogen on a catalyst, comprising, in a body (21) of the burner (20) a first self - ignition catalyst (23) and a subsequent group of oxidation catalysts (26), as well as comprising a heat exchanger (35) heated by the burnt gases, wherein in the burner (20) the heat exchanger (35) is obtained as a common heat exchanger and it is arranged outside the body (21) of the burner (20) accommodating the catalysts (23, 26). A head (22) accommodating the self - ignition catalyst (23) may be separated by a body (40) accommodating the oxidation catalysts (26). A second heat exchanger, passed through by cold water, allows production of high purity distilled water. In the proposed boiler a first part accommodates the burner modules (20) and another part accommodates the common heat exchanger (35) and the possible additional heat exchanger for producing distilled water.