The photoproduction of the omega meson has been studied at GRAAL from threshold up to a photon energy of 1.5 GeV. The differential cross sections and beam asymmetries have been measured precisely at all angles. The total cross section is also obtained. Systematic enhancements of the differential cross section at large angles and nonzero beam asymmetries at intermediate angles provide clear evidence for s- and u-channel resonant processes. The data are compared to the results of hadron and quark models.