This talk is an introduction to Grothendieck's Anabelian Geometry. The philosophy of the subject is that under certain hyperbolicity conditions it should be possible to recover an algebraic variety from it fundamental group. We will also discuss how the Tate Conjecture, in the case of elliptic curves, can be viewed as a type of Grothendieck Conjecture in Anabelian Geometry. Sources for this talk are a Preprint of S.Mochizuki and a survey paper by F. Pop.