  We extend the concept of Segre's Invariant to vector bundles on a surface
$X$. For $X=\mathbb{P}^2$ we determine what numbers can appear as the Segre
Invariant of a rank $2$ vector bundle with given Chern's classes. The
irreducibility of strata with fixed Segre's invariant is proved and its
dimensions are computed. Finally, we present applications to the
Brill-Noether's Theory for rank $2$ vector bundles on $\mathbb{P}^2.$
