Monolayer mixtures of arachidic (eicosanoic) acid with cholesterol are investigated on a subphase of pH 12.0 at 25 degrees C using grazing incidence X-ray diffraction (GID) and Brewster angle microscopy (BAM). GLD is applied in the low concentration range from 0 to 5 mol % cholesterol and reveals significant nonmonotonic changes in the dependence of the mean molecular area and the crystallinity (expressed by the position correlation length) of the monolayer on the cholesterol concentration. The condensation and lattice order strongly depend on the surface pressure. At zero pressure, condensation and lattice order are relatively large below 1 mol % cholesterol and decrease with increasing cholesterol concentration. At high pressure, this behavior is reversed. These cholesterol effects are compared with those observed in phospholipid bilayers, which are not yet completely understood. With BAM, the formation of domains and the phase separation of arachidic acid and cholesterol is observed with 1-20 mol % cholesterol. The shape of the domains is different from that in the absence of cholesterol, which is attributed to the "line activity" of cholesterol rather than to structural changes. The isolation of the domains embedded in a condensed matrix allows the observation of the recovery of the inner domain structure with variation of the surface pressure.