  There is a growing interest in the logical possibility that exceptional
mathematical structures (exceptional Lie and superLie algebras, the exceptional
Jordan algebra, etc.) could be linked to an ultimate "exceptional" formulation
for a Theory Of Everything (TOE). The maximal division algebra of the octonions
can be held as the mathematical responsible for the existence of the
exceptional structures mentioned above. In this context it is quite motivating
to systematically investigate the properties of octonionic spinors and the
octonionic realizations of supersymmetry. In particular the $M$-algebra can be
consistently defined for two structures only, a real structure, leading to the
standard $M$-algebra, and an octonionic structure. The octonionic version of
the $M$-algebra admits striking properties induced by octonionic $p$-forms
identities.
