This book contains expository lectures from the CBMS Regional Conference held at the University of Florida, 1982. The author considers a space formed by all closed curves in which the closed geodesics are characterized as the critical points of a functional, an idea going back to Morse. This exposition gives a refined version of Morse's approach which has several advantages over the old one - in particular, it possesses a canonical $\mathbf O(2)$-action.
The Hilbert manifold of $H^1$-curves The loop space and the space of closed curves The second order neighborhood of a critical point Appendix. The $S^1$- and the $Z 2$-action on $\Lambda M$ Closed geodesics on spheres On the existence of infinitely many closed geodesics.