We present a catalogue of new spectral types for hot, luminous stars in the Small Magellanic Cloud. The catalogue contains 4161 objects, giving an order of magnitude increase in the number of SMC stars with published spectroscopic classifications. The targets are primarily B- and A-type stars (2862 and 853 objects respectively), with 1 Wolf-Rayet, 139 O-type, and 306 FG stars, sampling the main sequence to ~mid-B. The selection and classification criteria are described, and objects of particular interest are discussed, including UV-selected targets from the Ultraviolet Imaging Telescope (UIT) experiment, Be and B[e] stars, `anomalous A supergiants', and composite-spectrum systems. We examine the incidence of Balmer-line emission, and the relationship between H-gamma equivalent width and absolute magnitude for BA stars.