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Arbitrary diffeomorphically invariant metric-torsion theories of gravity areconsidered. It is assumed that Lagrangians of such theories contain derivativesof field variables (tensor densities of arbitrary ranks and weights) up to asecond order only. The generalized Klein-Noether methods for constructingmanifestly covariant identities and conserved quantities are developed.Manifestly covariant expressions are constructed without including auxiliarystructures like a background metric. In the Riemann-Cartan space, the following\emph{manifestly generally covariant results} are presented: (a) The completegeneralized system of differential identities (the Klein-Noether identities) isobtained. (b) The generalized currents of three types depending on an arbitraryvector field displacements are constructed: they are the canonical Noethercurrent, symmetrized Belinfante current and identically conservedHilbert-Bergmann current. In particular, it is stated that the symmetrizedBelinfante current does not depend on divergences in the Lagrangian. (c) Thegeneralized boundary Klein theorem (third Noether theorem) is proved. (d) Theconstruction of the generalized superpotential is presented in details, andquestions related to its ambiguities are analyzed.

Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. I. General Consideration