  A wardian calculus of sequences started almost seventy years ago constitutes
the general scheme for extensions of the classical umbral operator calculus
considered by many afterwards . At the same time this calculus is an example of
the algebraization of the analysis here restricted to the algebra of formal
series. This is a review article based on the recent first author
contributions. As the survey article it is supplemented by the short indicatory
glossaries of notation and terms used by prominent contributors to the domain.
