Apparatus for laser material processing comprising: a beam deflecting unit with at least one reflecting mirror configured as a rotating mirror or tilting mirror for deflecting a laser beam that defines a laser beam axis along a first direction relative to a surface of a workpiece to be processed for path guiding the laser beam on the surface of the workpiece, characterized by: a parallel-offsetting unit with at least three reflecting mirrors (26, 28, 30) for parallel offsetting the laser beam relative to an optical axis (oA) along a first parallel-offset direction, wherein one reflecting mirror of the at least three reflecting mirrors for parallel offsetting the laser beam is rotatable and the entry reflection and the exit reflection takes place at the rotatable, reflecting mirror, a further parallel-offsetting unit which is configured like the parallel-offsetting unit for parallel offsetting the laser beam along a second parallel-offset direction, wherein the parallel-offsetting units are optically coupled with each other such that the laser beam may be offset in parallel along two different parallel-offset directions, and a focusing device for focusing the laser beam which has been translated in parallel by the parallel-offsetting units and deflected by the beam deflecting unit onto the workpiece, wherein the angle of incidence of the laser beam axis on the workpiece can be varied by adjusting the parallel offsets performed by the parallel-offsetting units in two spatial directions. a beam deflecting unit with at least one reflecting mirror configured as a rotating mirror or tilting mirror for deflecting a laser beam that defines a laser beam axis along a first direction relative to a surface of a workpiece to be processed for path guiding the laser beam on the surface of the workpiece, characterized by: a parallel-offsetting unit with at least three reflecting mirrors (26, 28, 30) for parallel offsetting the laser beam relative to an optical axis (oA) along a first parallel-offset direction, wherein one reflecting mirror of the at least three reflecting mirrors for parallel offsetting the laser beam is rotatable and the entry reflection and the exit reflection takes place at the rotatable, reflecting mirror, a further parallel-offsetting unit which is configured like the parallel-offsetting unit for parallel offsetting the laser beam along a second parallel-offset direction, wherein the parallel-offsetting units are optically coupled with each other such that the laser beam may be offset in parallel along two different parallel-offset directions, and a focusing device for focusing the laser beam which has been translated in parallel by the parallel-offsetting units and deflected by the beam deflecting unit onto the workpiece, wherein the angle of incidence of the laser beam axis on the workpiece can be varied by adjusting the parallel offsets performed by the parallel-offsetting units in two spatial directions. a parallel-offsetting unit with at least three reflecting mirrors (26, 28, 30) for parallel offsetting the laser beam relative to an optical axis (oA) along a first parallel-offset direction, wherein one reflecting mirror of the at least three reflecting mirrors for parallel offsetting the laser beam is rotatable and the entry reflection and the exit reflection takes place at the rotatable, reflecting mirror, a further parallel-offsetting unit which is configured like the parallel-offsetting unit for parallel offsetting the laser beam along a second parallel-offset direction, wherein the parallel-offsetting units are optically coupled with each other such that the laser beam may be offset in parallel along two different parallel-offset directions, and a focusing device for focusing the laser beam which has been translated in parallel by the parallel-offsetting units and deflected by the beam deflecting unit onto the workpiece, wherein the angle of incidence of the laser beam axis on the workpiece can be varied by adjusting the parallel offsets performed by the parallel-offsetting units in two spatial directions.