In the study of closed geodesics the free loop space A(M)={c: S1--,M} is a natural tool. It can be made into a Hilbert manifold and the energy integral is a C ~ function on A(M) whose critical points are the closed geodesics. Therefore Morse theory has been applied to find relationships between closed geodesics and the topology of A(M). The most important application is the theorem of Gromoll-Meyer [9] proving the existence of infinitely many closed geodesics under certain weak conditions on the topology of A(M). But one can also apply this theory the other way around by computing the homology of A(M) if one knows the closed geodesics for a sufficiently nice metric. This is done here for a globally symmetric M. It is shown that the critical points in A(M) form nondegenerate critical submanifolds whose index can be computed in terms of the roots of M, and that the relative homology appearing in Morse theory survives in all of A(M), at least for Z 2 coefficients. Thus the roots of M determine H,(A(M), Z2) completely, and it is easy to show that the Betti numbers bi(A(M), Z2) are unbounded if M has rank >1. This in turn implies that for any riemannian metric on M there exist infinitely many closed geodesics by the Gromoll-Meyer theorem. In proving that the citical submanifolds are nondegenerate we also compute the Poincare map of a closed geodesic and show that it has a particularly simple form. In 1.1 we shortly describe Morse theory on A(M), in 1.2 we introduce the Poincare map of a closed geodesic, and in 1.3 we collect a few facts about globally symmetric spaces with some simple consequences for closed geodesics. In 2.1 we determine the Poincare map of a closed geodesic which can be used at the same time to show that all critical submanifolds are nondegenerate. In 2.2 the index of a closed geodesic is calculated, and in 2.3 this is interpreted in terms of the roots of M with the consequence that the index of a closed geodesic turns out to be equal to the number of conjugate points. In 3.1 we show that the relative homology survives for Z 2 coefficients which is used in 3.2 to estimate the Betti numbers bi(A(M ), Z2). The consequence for the existence of infinitely many closed geodesics is discussed.