Using the EPIC and RGS data from a deep (~200 ks) XMM-Newton observation, we investigate the temperature structure (kT and sigma_T ) and the abundances of 9 elements (O, Ne, Mg, Si, S, Ar, Ca, Fe and Ni) of the intra-cluster medium (ICM) in the nearby (z=0.046) cool-core galaxy cluster Abell 4059. Next to a deep analysis of the cluster core, a careful modelling of the EPIC background allows us to build radial profiles up to 12' (~650 kpc) from the core. Probably because of projection effects, the temperature ICM is found not to be in single phase, even in the outer parts of the cluster. The abundances of Ne, Si, S, Ar, Ca and Fe, but also O are peaked towards the core. Fe and O are still significantly detected in the outermost annuli; suggesting that the enrichment by both type Ia and core-collapse SNe started in the early stages of the cluster formation. However, the particularly high Ca/Fe ratio that we find in the core is not well reproduced by the standard SNe yield models. Finally, 2-D maps of temperature and Fe abundance are presented and confirm the existence of a denser, colder, and Fe-rich ridge southwest of the core, previously observed by Chandra. The origin of this asymmetry in the hot gas of the cluster core is still unclear, but might be explained by a past intense ram-pressure stripping event near the central cD galaxy. ; Comment: 17 pages, 13 figures, accepted for publication in A&A