  The use of algebraic tools of operational and umbral nature is exploited to
develop a new point of view and to extend the theory of Hermite polynomials,
with more than one variable also of complex nature. The techniques we adopt
includes multivariable/many index Hermite- Kampe-de-Feriet polynomials of order
two and higher. It will be shown that the treatment, foreseen here, simplifies
the study of the relevant properties and the associated computational
technicalities.
