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It is the purpose of the present paper to outline an introduction in theoryof embeddings in the manifold Osc^{2}M. First, we recall the notion of2-osculator bundle. The second section is dedicated to the notion ofsubmanifold in the total space of the 2-osculator bundle, the manifoldOsc^{2}M. A moving frame is constructed. The induced N-linear connections andthe relative covariant derivatives are discussed in third and fourth sections.The Ricci identities of the Liouville d-vector fields are present in the lastsection.

Ricci identities of the Liouville d-vector fields z^(1)alpha and z^(2)alpha