This Seminar has been organized in Erice, in the frame of the Eloisatron project activities, with the special purpose of bringing together an interdisciplinary group of distinguished physicists with prominent interest in the development of the accelerators. Listening to the invited lectures, examining the new topics and reviewing ideas for the acceleration of particles to energies beyond those attainable in machines whose construction is under way or is now contemplated are all important moments of this Seminar that will offer to the Italian Physicists a very important opening over the...