In this paper, the concepts of “partial parallelizable manifold” and “partial trivial tangent bundle” are fundamental notions. The aim of this paper is to obtain some properties about partial parallelizable manifolds (M, ρ_p) and their relations to integrable partial trivial structures in tangent bundle. In the study of the couple (M, ρ_p) an important operation on ρ_p is the construction of other geometric and topological objects: G(M)−invariants, homotopy invariants and their relations with Pontryagin classes of the tangent bundle TM. We give a description of Pontryagin algebra of the partial trivial tangent vector bundle of M: if F is a foliation of M, we show that TM is null in dimension d > 2 (m − p), where m = dim M and p = dim F . The case of integrable partial trivial structures is considered. If the subbundle E (ρ_p) generated from ρ_p is integrable, then there is a G(M)-invariant [M(ρ_p)] associated with (M, ρ_p). Finally, we give some examples.