The high resolution VUV photoabsorption spectrum of dimethyl sulphoxide is reported in the wavelength range 115-340 nm (10.8-3.7 eV). The result is compared with previous electron energy loss spectra and low resolution VUV studies. Electronic state assignments have been suggested for each of the observed absorption bands incorporating both valence and Rydberg transitions. Many of the Rydberg features are seen here for the first time. Four Rydberg transitions have been assigned converging to the first ionisation limit at 9.1 eV, and a further five Rydberg transitions have been assigned converging to the second ionisation limit (10.1 eV). The high resolution achieved has allowed vibrational series to be assigned for the first time. The measured VUV cross sections may be used to derive the photolysis rate of (CH3)(2)SO in the terrestrial atmosphere.