Atomic sulphur adsorbed on Ru(001) was investigated by LEED and AES. It produces a sequence of 5 ordered commensurate structures. After formation of p(2x2)-ordered islands at coverages 0.1 < theta < 0.2, a homogeneous p(2x2) phase follows. Atoms added to the completed p(2x2) structure form (square-root 3 x square-root 3)R30-degrees ordered islands which coexist with the p(2X2) structure for 0.26 < theta < 0.32. Addition of only 0.01 monolayer to the completed (square-root 3 x square-root 3)R30-degrees phase causes the formation of (disordered) line defects which order at coverages above theta = 0.35 and form superheavy domain walls with striped symmetry ending in a c(2x4) structure (0.48 < theta < 0.52). At increasing coverages an only short-range ordered fluid phase, stable up to theta = 0.54, is followed by two commensurate phases, a (7/3 0/6) phase and a (square-root 7 x square-root 7)R19.1-degrees phase with maximum thermal stability of the latter at theta = 0.57. Both structures coexist in a small range of coverage. The superstructure beams of the latter split above theta = 0.59. A further increase of theta leads to disappearance of split beams so that the sulphur layer is disordered for coverages above 0.61 at all temperatures. A second S-layer is formed at coverages higher than theta = 0.62. The complete phase diagram was determined and is discussed in detail.