A conjecture of Berger says that on a simply connected manifold all of whose geodesics are closed, all geodesics are closed with the same length. In this thesis we will prove that this conjecture holds for three dimensional manifolds. Namely we will show that the $\IS^1$-action induced by the geodesic flow is free. This is done in two parts. First we do some cohomological computations involving the Morse theory of the free loop space of $M$. Secondly we use methods from symplectic geometry and topology to investigate the topology of the quotient of the unit tangent bundle $T^1M/\IS^1$ by the $\IS^1$ action that comes from the geodesic flow. We show that this quotient admits the structure of a smooth symplectic manifold and that this symplectic manifold is symplectomorphic to $\IS^2\times \IS^2$ equipped with a split form. These two approaches lead at the end to a solution of Berger's conjecture, when the underlying manifold is three dimensional.