The method of cutting a transparent surface such as the eye involves generating optical cuts in the material using laser beams focussed on the material. The focal point is adjusted to form the cuts by a flat grid type arrangement of optical cuts. The focal point is adjusted along a line. Adjacent optical cuts along the line are not formed directly one behind the other. The grid type arrangement is made up of at least two partial grids which, as regards their optical cuts, are processed successively. An independent claim is included for an apparatus for carrying out the method.
