M75 is a relatively young Globular Cluster (GC) found at 15kpc from the Galactic centre at the transition region between the inner and outer Milky Way halos. 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. 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). We present the first comprehensive abundance study of M75 to date. The cluster is metal-rich ([Fe/H]=-1.16+/-0.02dex, [alpha/Fe]=+0.30+/-0.02dex), and shows a marginal spread in [Fe/H] of 0.07dex, 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 0.6dex, respectively, indicative of pollution by lower mass (M~4-5M_{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.