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On a differentiable manifold M endowed with a Riemannian metric or Finsler metric the geodesics determine a dynamical system on the unit tangent bundle.The periodic orbits correspond to the closed resp.periodic geodesics.Closed geodesics are the critical points of the energy functional E on the free loop space ΛM.One can consider the energy functional as a generalized Morse function.Using the topology of the free loop space one obtains existence results for closed geodesics.We will show that a compact and simply-connected manifold with a generic Riemannian metric carries infinitely many closed geodesics.In contrast there are non-reversible Finsler metrics carrying only finitely many closed geodesics.These metrics lead to resonance phenomena which can be explained using product structures on the homology of the free loop space introduced in string topology.In this mini-course we plan to address the following topics: 1.Geodesics in Riemannian and Finsler Geometry 2.Equivariant Morse Theory and the Topology of the Free Loop Space 3.Existence Results for Closed Geodesics 4.Resonance Phenomena.