  This paper provides a description of an algebraic setting for the Lagrangian
formalism over graded algebras and is intended as the necessary first step
towards the noncommutative C-spectral sequence (variational bicomplex). A
noncommutative version of integration procedure, the notion of adjoint
operator, Green's formula, the relation between integral and differential
forms, conservation laws, Euler operator, Noether's theorem is considered.
