Abstract: In arbitrary Riemannian 4-spaces, continuity equations are constructed which could be interpreted as conservation laws for the energy and momentum of the gravitational field. Special attention is given to general relativity to obtain, of natural manner, the pseudotensors of Einstein, Landau-Lifshitz, Möller, Goldberg and Stachel, and also the conservation equations of Komar, Trautman, DuPlessis and Moss.

Key words: Noether theorem, Lagrangians in curved spaces, Energy and momentum in Riemannian spaces, Rund-Lovelock identities

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