A geometric approach to qualitative problems in intrinsic differential geometry" would be a brief description of the present book, which extends the methods developed in the author's "Metric Methods in Finsler Spaces and in the Foundations of Geometry," Princeton, 1942. In the earlier book the emphasis was on spaces in which the geodesic through two points is unique, whereas it is now on the general case in which the geodesies have only local uniqueness properties. Consequently, the relations to the foundations of geometry are no longer very relevant and Finsler spaces are the principal subject. For two reasons the latter do not appear in the title: Firstly, "Geometry of Geodesies" expresses clearly the method of attack and the intrinsic aspect. Secondly, the term Finsler Space means to many not only a type of space but also a definite approach: The space is considered as a set of line elements to which euclidean metrics are attached. The main problems are connected with parallelism. In spite of the great success of Finsler's thesis, the later development of this aspect lacks simple geometric facts to the extent that their existence in non-Riemannian geometry has been doubted.
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