Introduction 1
Chapter 1. The Hubert manifold of i^-curves 3
Chapter 2. The loop space and the space of closed curves 15
Chapter 3. The second order neighborhood of a critical point 25
Appendix. The S1- and the Z2-action on AM 39
Chapter 4. Closed geodesics on spheres 45
Chapter 5. On the existence of infinitely many closed geodesics 59
References 77
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