  In 1932 Ettore Majorana published an article proving that relativity allows
any value for the spin of a quantum particle and that there is no privilege for
the half integer spin. The Majorana idea was so innovative for the time that
the scientific community understood its importance only towards the end of the
thirties. This paper aims to highlight the depth of the scientific thought of
Majorana that, well in advance of its time, opened the way for modern particle
physics and introduced for the first time the idea of a universal quantum
equation, able to explain the behavior of particles with arbitrary spin and of
any nature, regardless the value of their speed. It will be analyzed in detail
and made explicit all the steps that lead to the physical mathematical
formulation of the Majorana theory. A part of these steps require basic
knowledge of quantum physics but not for this should be regarded as trivial
since they show the physical meaning hidden into the structure of the equation.
Moreover, the explicit method for the construction of the infinite matrices
will be given, by which the infinite components of the wave functions
representing the fundamental and excited states of the particle are calculated.
