The most basic examples of submanifold with curvature bounded below are probably hypersurface with positive sectional curvature in Euqlidea space. These surface are locally convex, i.e, each point has a neighborhood which lies locally on one side of its tangent plane. In this Thesis, the finiteness theorem states that a smooth compact submanifold of codimension 2 immersed in Euqlidean space. For n greater or equal 3, bounds at most finitely many topologically distinct compact non negatively curved hypersurface . To this end, we define Alexandrov spaces of curvature greater or equal to K , then, we will prove the finiteness theorem by use of this notion. Specifically in this space for any geodesic triangle the distance from a vertex to a point on the opposite of side is at least the distance between corres ponding point on a geodesic triangle with the same side length in the simply connected space of constant curvature K. Under greater regularity and by use of ltr"
