The cosmic radiation is a rain of atomic nuclei and electrons which continuously cross any region of the Milky Way Galaxy, and in particular, the Earth surface. The energies of the cosmic particles range from those of the quiescent matter up to the maximum energies observed in Nature, which presently are about ten thousand times higher than those produced in terrestrial laboratories by the most powerful particle accelerators. In the last years, following the measurements of some experiments, almost all the fundamental ideas and theories on the cosmic radiation recurrent in the literature have been proved to be inadequate to describe the experimental data. This booklet reports a survey of some new ideas and calculations to account for the observed characteristic features of the cosmic radiation along with a critical examination of the experimental data which prompted a scientific revolution in Cosmic Ray Physics.