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The concepts of L-equivalence of submanifolds (due to R. Thom) and ambiental bordism of submanifolds will be the main objects of this thesis. Let Nⁿ be an oriented manifoid, L_k(N) the set of L-equivalence classes of compact oriented submanifolds K^k ⊂ N and Ω_k (N) the K^th oriented bordism group of N. There is a natural map Φ : L_k (N) → Ω_k (N). One of the main results is the following theorem: "If n ≥ 2k, there is a geometric group structure on L_k(N) such that Φ is an isomorphism. In particular, if N = S^2k there is an isomorphism π_2K(MS0(k)) ≈ Ω_k". The main result about ambiental bordism is the following: Let n = 2k+1, Nⁿ a compact oriented manifold and K^k a compact oriented submanifold of N. Then K bounds in N if and only if Φ([K]) = O, where [K] is the L-equivalence class of K".