PUMA, antiProton Unstable Matter Annihilation, is a nuclear-physics experiment at CERN aiming at probing the surface properties of stable and rare isotopes by use of low-energy antiprotons. Low-energy antiprotons offer a very unique sensitivity to the neutron and proton densities at the annihilation site, i.e. in the tail of the nuclear density. Today, no facility provides a collider of low-energy radioactive ions and low-energy antiprotons: while not being a collider experiment, PUMA aims at transporting one billion antiprotons from ELENA, the Extra-Low-ENergy Antiproton ring, to ISOLDE, the rare-isotope beam facility of CERN. PUMA will enable the capture of low-energy antiprotons by short-lived nuclei and the measurement of the emitted radiations. In this way, PUMA will give access to the so-far largely unexplored isospin composition of the nuclear-radial-density tail of radioactive nuclei. The motivations, concept and current status of the PUMA experiment are presented.