Apparatus for laser material processing, comprising: a beam deflecting unit with a first reflecting mirror designed as a rotating mirror or tilting mirror for deflecting a laser beam, which defines a laser beam axis, along a first direction relative to a workpiece to be processed and a second reflecting mirror designed as a rotating mirror or tilting mirror for deflecting the laser beam along a second direction relative to the workpiece for guiding the path of the laser beam on a workpiece surface, characterized by: a parallel offsetting unit having three reflecting mirrors (26, 28, 30) for parallel offsetting of the laser beam relative to an optical axis (oA), along a first parallel offset direction, wherein one reflecting mirror of the three reflecting mirrors is rotatable for parallel offsetting of the laser beam, and the entry reflection and the exit reflection take place at the rotatable, reflecting mirror, wherein two of the three reflecting mirrors are fixed mirrors (28, 30), and wherein the parallel offsetting unit is configured such that the laser beam is reflected four times by means of the mirror arrangement, wherein the parallel offsetting unit is configured to parallel offset laser beams exiting the parallel offsetting unit relative to each other depending on the angle of rotation of the rotatable mirror of the parallel offsetting unit, a focusing device for focusing the laser beam, which is shifted in parallel by means of the parallel offsetting unit and deflected by means of the beam deflecting unit, onto the workpiece, wherein an incidence angle of the laser beam axis on the workpiece is variable by setting the parallel shift which takes place by means of the parallel offsetting unit, and a controller which is configured such that a synchronized control of the beam deflecting unit and the parallel offsetting unit is implemented. a beam deflecting unit with a first reflecting mirror designed as a rotating mirror or tilting mirror for deflecting a laser beam, which defines a laser beam axis, along a first direction relative to a workpiece to be processed and a second reflecting mirror designed as a rotating mirror or tilting mirror for deflecting the laser beam along a second direction relative to the workpiece for guiding the path of the laser beam on a workpiece surface, characterized by: a parallel offsetting unit having three reflecting mirrors (26, 28, 30) for parallel offsetting of the laser beam relative to an optical axis (oA), along a first parallel offset direction, wherein one reflecting mirror of the three reflecting mirrors is rotatable for parallel offsetting of the laser beam, and the entry reflection and the exit reflection take place at the rotatable, reflecting mirror, wherein two of the three reflecting mirrors are fixed mirrors (28, 30), and wherein the parallel offsetting unit is configured such that the laser beam is reflected four times by means of the mirror arrangement, wherein the parallel offsetting unit is configured to parallel offset laser beams exiting the parallel offsetting unit relative to each other depending on the angle of rotation of the rotatable mirror of the parallel offsetting unit, a focusing device for focusing the laser beam, which is shifted in parallel by means of the parallel offsetting unit and deflected by means of the beam deflecting unit, onto the workpiece, wherein an incidence angle of the laser beam axis on the workpiece is variable by setting the parallel shift which takes place by means of the parallel offsetting unit, and a controller which is configured such that a synchronized control of the beam deflecting unit and the parallel offsetting unit is implemented. a parallel offsetting unit having three reflecting mirrors (26, 28, 30) for parallel offsetting of the laser beam relative to an optical axis (oA), along a first parallel offset direction, wherein one reflecting mirror of the three reflecting mirrors is rotatable for parallel offsetting of the laser beam, and the entry reflection and the exit reflection take place at the rotatable, reflecting mirror, wherein two of the three reflecting mirrors are fixed mirrors (28, 30), and wherein the parallel offsetting unit is configured such that the laser beam is reflected four times by means of the mirror arrangement, wherein the parallel offsetting unit is configured to parallel offset laser beams exiting the parallel offsetting unit relative to each other depending on the angle of rotation of the rotatable mirror of the parallel offsetting unit, a focusing device for focusing the laser beam, which is shifted in parallel by means of the parallel offsetting unit and deflected by means of the beam deflecting unit, onto the workpiece, wherein an incidence angle of the laser beam axis on the workpiece is variable by setting the parallel shift which takes place by means of the parallel offsetting unit, and a controller which is configured such that a synchronized control of the beam deflecting unit and the parallel offsetting unit is implemented.