  Context: M 75 is a relatively young Globular Cluster (GC) found at 15 kpc
from the Galactic centre at the transition region between the inner and outer
Milky Way halos. Aims: Our aims are to perform a comprehensive abundance study
of a variety of chemical elements in this GC such as to investigate its
chemical enrichment history in terms of early star formation, and to search for
any multiple populations. Methods: We have obtained high resolution
spectroscopy with the MIKE instrument at the Magellan telescope for 16 red
giant stars. Their membership within the GC is confirmed from radial velocity
measurements. Our chemical abundance analysis is performed via equivalent width
measurements and spectral synthesis, assuming local thermodynamic equilibrium
(LTE). Results: We present the first comprehensive abundance study of M 75 to
date. 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. A moderately extended O-Na
anticorrelation is clearly visible, likely showing three generations of stars,
formed on a short timescale. Additionally the two most Na-rich stars are also
Ba-enhanced by 0.4 and 0.6 dex, respectively, indicative of pollution by lower
mass (M ~ 4-5 M_Sun) Asymptotic Giant Branch (AGB) stars. The overall n-capture
element pattern is compatible with predominant r-process enrichment, which is
rarely the case in GCs of such a high metallicity.
