The invention relates to a compact reactor that consists of a number of plates that are arranged like stacks and spaced some distance apart, whereby a) The plates are separated by spacers and are sealed off from one another in a gas-tight manner, b) The plates are profiled in the shape of waves, so that flow channels are formed by the wave troughs that are separated from one another by the wave crests (fins), c) The flow channels run parallel to one another and parallel to one side of the plate, d) The flow channels at least partially contain at least one catalyst material that is introduced such that gaseous and/or liquid media can flow through the flow channels, and e) The compact reactor has means (headers) for feeding at least two gaseous and/or liquid media to the flow channels or removing them therefrom. The invention also relates to the use of a compact reactor. The gaseous and/or liquid medium that flows in the flow channels can flow through the fins between the individual flow channels of a plate.