Abstract: In this work, the geometry of the almost complex substructures, that is the geometry of the 

subbundles of the tangent bundle of the manifolds carrying almost complex structures is studied. 

The analogues of the geometric results about the almost complex structures which exists on the whole 

tangent bundle of a manifold is obtained in the case of almost complex substructures. These substructures 

are studied when they are without any other structure, when they carry a suitable  metric 

(partially Hermitian metric), and when they carry a suitable connection (partially unitary connection).