NEUTRINOS and DARK MATTER (DM) are the most abundant and also the most elusive building-blocks of nature because of their tenuous couplings to the ordinary matter we are made of. Each particle has a mirror image with identical mass and opposite charge: its antiparticle. What is the essential nature of particles and antiparticles? This is a most fundamental open question in science. The laws of physics are almost -but not quite- symmetric for particles and antiparticles, and this could explain why the universe is made of matter, i.e. why we are here. Tiny differences detected in visible matter are largely insufficient, while an asymmetric behaviour of neutrinos or of DM may be the seed. In turn, the unnaturally symmetric behaviour of strong interactions points to a new particle, the axion, also a superb DM candidate. For the first time, the connection between these asymmetries in the visible and invisible world will be addressed. Very timely, an ambitious experimental search of asymmetric behaviour has been launched on neutrinos, axions and other DM, and the Higgs, with imminent major breakthroughs. The path to understand the Universe and build the New Standard Model must confront this problem. The mission of Elusives ITN is to form the new generation of researchers to accomplish this task, focusing on phenomenology with the necessary link to experiment. This is the first transnational such program, exploiting the capital investment in new experiments and overcoming the fragmentation of the research effort. ELUSIVES ITN is uniquely placed for it: * World-leadership in all relevant areas; * Multidisciplinarity; * Key theorists and experimentalists; * Outstanding training record; * CERN, Fermilab, SuperKamiokande and ADMX partners; * World leading cutting-edge research-related industry; * Highest professional beneficiary dissemination; * Top-quality expertise from emerging countries; * Optimal gender balance with over 50% female international leaders as coordinators.