The origin of the spin concept was probably the most complicated of all the quantum physics. Indeed, after Bohr's triumph in 1913, Bohr and Sommerfeld's "old quantum theory'', based on the idea of quantum restrictions applied to classical magnitudes, gave a unified explanation of the spectroscopic data. Atomic physics shows that it is not possible to account for the observed effects if we assume that the electron, a point particle, and the three degrees of freedom of translation in space that we have considered up to now. In quantum relativistic mechanics, the structure of the Lorentz group reveals the kinetic momentum to any particle as an intrinsic attribute, which is defined in the same way as its electric charge and its mass. There are several possible representations of the states, accompanied by corresponding representations of the observables, whose use can be more or less convenient according to the problem under consideration.