The structure of grain boundaries can be represented by means of the O-lattice method in terms of dislocation networks. The physical guide-line behind these considerations is that, in the boundary, certain structures, i.e. "preferred states" are conserved. The "primary preferred state" is the single crystal state, while "secondary preferred states" are periodic patterns in the boundary which are formed in certain coincidence orientations. While the dislocations are discrete jumps (quanta) of displacement, the areas within the meshes of the dislocation network are in the preferred state which may, however, be somewhat elastically distorted. The example treated is a boundary in aluminium close to a Σ = 59 orientation