We present the abundance analysis for a sample of 17 red giant branch stars in the metal-poor globular cluster M28 based on high-resolution spectra. This is the first extensive spectroscopic study of this cluster. We derive abundances of O, Na, Mg, Al, Si, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Ba, La, Ce, and Eu. We find a metallicity of [Fe/H]=-1.29+/-0.01 and an {alpha}-enhancement of +0.34+/-0.01 (errors on the mean), typical of halo globular clusters in this metallicity regime. A large spread is observed in the abundances of light elements O, Na, and Al. Mg also shows an anti-correlation with Al with a significance of 3{sigma}. The cluster shows a Na-O anti-correlation and a Na-Al correlation. This correlation is not linear but 'segmented' and that the stars are not distributed continuously, but form at least three well-separated sub-populations. In this aspect, M28 resembles NGC 2808 that was found to host at least five sub-populations. The presence of a Mg-Al anti-correlation favour massive AGB stars as the main polluters responsible for the multiple-population phenomenon.