  We present the first comprehensive abundance study of the massive, outer halo
globular cluster (GC) M 75 (NGC 6864). This unique system shows a very extended
trimodal horizontal branch (HB), but no other clues for multiple populations
have been detected in its colour-magnitude diagram (CMD). Based on
high-resolution spectroscopic observations of 16 red giant stars, we derived
the abundances of a large variety of alpha, p-capture, iron-peak, and n-capture
elements. We found that the cluster is metal-rich ([Fe/H] = -1.16 +/- 0.02 dex,
[alpha/Fe] = +0.30 +/- 0.02 dex), and shows a marginal spread in [Fe/H] of 0.07
dex, typical of most GCs of similar luminosity. We detected significant
variations of O, Na, and Al among our sample, suggesting three different
populations. Additionally, the two most Na-rich stars are also significantly
Ba-enhanced, indicating a fourth population of stars. Curiously, most stars in
M 75 (excluding the two Ba-rich stars) show a predominant r-process enrichment
pattern, which is unusual at the cluster's high metallicity. We compare the
abundance properties of M 75 and NGC 1851 (a GC very similar to M 75 in terms
of age, metallicity, and HB morphology) and draw conclusions on M 75's possible
formation scenarios.
