Reactor with multilayer structure comprising - an upper fluid-tight cover layer, - a lower fluid-tight cover layer, - fluid-tight side walls and at least one reaction space located therebetween, which is defined by several superimposed structural layers parallel to the cover layers, wherein - the individual structural layers each have a structure of parallelograms arranged periodically in several rows, each arranged edge-to-edge, and wherein the areas of the parallelograms are designed as openings and their edges are designed as webs, - each structural layer is offset by a factor of 0.5±0.2 and 0.5±0.2 in the x and y directions relative to the layer above and below it respectively, wherein the largest edge length of the parallelograms is standardised as 1 and specifies the x direction and the y direction is orthogonal to this in the plane of the structural layer, - the side edges of the parallelogram structures in the structure layers are arranged rotated by 30 to 60° in relation to the front and rear sides of the reactor, resulting in incomplete parallelogram structures with openings not completely surrounded by webs at the front and rear sides of the reactor, - the reaction space is laminary flowed against from the front side of the reactor, wherein the flowing-against fluid flows into the openings that are not completely surrounded by webs, - the front and rear sides of the reactor are configured for the inflow and outflow of reaction medium, - the cover and structural layers are made of material with good thermal conductivity, - the contact points and areas of the webs of the superimposed structural layers are fully connected to each other, - catalyst bed can be arranged, preferably is arranged, in the openings between the webs of the structural layers, - and wherein the overlap of the openings of one layer by the webs of the overlying layer is 30-60%, and - wherein the material with good thermal conductivity is a material with a thermal conductivity of from 10 to 400 W/(mK). - an upper fluid-tight cover layer, - a lower fluid-tight cover layer, - fluid-tight side walls - the individual structural layers each have a structure of parallelograms arranged periodically in several rows, each arranged edge-to-edge, and wherein the areas of the parallelograms are designed as openings and their edges are designed as webs, - each structural layer is offset by a factor of 0.5±0.2 and 0.5±0.2 in the x and y directions relative to the layer above and below it respectively, wherein the largest edge length of the parallelograms is standardised as 1 and specifies the x direction and the y direction is orthogonal to this in the plane of the structural layer, - the side edges of the parallelogram structures in the structure layers are arranged rotated by 30 to 60° in relation to the front and rear sides of the reactor, resulting in incomplete parallelogram structures with openings not completely surrounded by webs at the front and rear sides of the reactor, - the reaction space is laminary flowed against from the front side of the reactor, wherein the flowing-against fluid flows into the openings that are not completely surrounded by webs, - the front and rear sides of the reactor are configured for the inflow and outflow of reaction medium, - the cover and structural layers are made of material with good thermal conductivity, - the contact points and areas of the webs of the superimposed structural layers are fully connected to each other, - catalyst bed can be arranged, preferably is arranged, in the openings between the webs of the structural layers, - and wherein the overlap of the openings of one layer by the webs of the overlying layer is 30-60%, and - wherein the material with good thermal conductivity is a material with a thermal conductivity of from 10 to 400 W/(mK). <EOS>