0. Introduction. 1.Basic facts about the geodesic flow. 2.The manifolds of geodesics. 3.Compact symmetric spaces of rank one from a geometric point. 4.Some examples of C-and manifolds: Zoll and tannery surfaces. 5.Blaschke’s conjecture. 6.Harmonic manifolds. 7.On the topology of SC- and manifolds. 8.The spectrum of P-manifolds.