The purpose of the Symposium is to discuss the origin, the status and the future of the new frontier of Physics, the Subnuclear World, whose first two hints were discovered in the middle of the last century: the so-called “Strange Particles” and the “Resonance Δ++”. It took more than two decades to understand the real meaning of these two great discoveries: the existence of the Subnuclear World with regularities, spontaneously plus directly broken Symmetries, and totally unexpected phenomena including the existence of a new fundamental force of Nature, called Quantum ChromoDynamics. In order to reach this new frontier of our knowledge, new Laboratories were established all over the world, in Europe, in USA and in the former Soviet Union, with thousands of physicists, engineers and specialists in the most advanced technologies, engaged in the implementation of new experiments of ever increasing complexity. At present the most advanced Laboratory in the world is CERN where experiments are being performed with the Large Hadron Collider (LHC), the most powerful collider in the world, which is able to reach the highest energies possible in this satellite of the Sun, called Earth. Understanding the laws governing the Space-time intervals in the range of 10−17 cm and 10−23 sec will allow our form of living matter endowed with Reason to open new horizons in our knowledge.