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We intend to show the equivalence of the concepts of orientability and degree from the points of view of Algebraic Topology and Differential Topology. First, we give a natural correspondence between orientations in a tangent space TM_x, of a differentiable manifold Mⁿ and generators in H_n (M, M-x; Z). Then we show the equivalence of orientation in Differential and Algebraic Topology. If M is a compact, connected, oriented manifold, we assign for each point x in M a correspondence between the orientation classes of TM_x, and the generators of the infinite cyclic group H_n(M). It is done by using the isomorphism J_x : H_n(M) → H_n (M, M-x) such that J_x(μ_M) = μ_x, where μ_M is the fundamental homology class of M and μ_x, is à local orientation in x. Finally we show that under certain assumptions, the differentiable degree and the topological degree of f : M^m → Nⁿ are equivalent.