The invention relates to a heat exchanger, particularly of cross-current design, through which at least two separate media can flow. It comprises plates which are stacked on one another and which are spaced apart from one another in some areas and are in contact with one another in other areas, so that flow paths are formed between respectively adjacent plates in a heat exchange region. The plates have apertures adjacent to the heat exchange region, and the plates are spaced apart from one another by means of shaped-out portions of the plates. Areas succeeding one another about the circumference of the plates have apertures, and these areas are alternately shaped out in opposite directions from the plane of the plates.