Abstract
Contact structures for 3-manifolds can be understood as maximal families of plane distributions of non-integrable planes, while open book decompositions come from fiber bundles over S^1 on the complement of a link in a manifold. The theorem of correspondence of Giroux gives an closed relation between both concepts, allowing us to use mixed technique in the study of 3-manifolds and links contained in them.
We are going to introduce both techniques, and show how Gioux Theorem has been implemented to answer fundamental quiestions related to branch coverings over braids,and particularly in the problem of contact universal links and knots in S^3. Given this way, some open problems in the area.
