  Paragrassmann algebras with one and many paragrassmann variables are
considered from the algebraic point of view without using the Green ansatz.
Operators of differentiation with respect to paragrassmann variables and a
covariant para-super-derivative are introduced giving a natural generalization
of the Grassmann calculus to a paragrassmann one. Deep relations between
paragrassmann algebras and quantum groups with deformation parameters being
roots of unity are established.
