The aim of this book is to present the fundamental concepts and properties of the geodesic flow
of a closed Riemannian manifold. The topics covered are close to my research interests. An
important goal here is to describe properties of the geodesic flow which do not require
curvature assumptions. A typical example of such a property and a central result in this work
is Mane's formula that relates the topological entropy of the geodesic flow with the
exponential growth rate of the average numbers of geodesic arcs between two points in the
manifold. The material here can be reasonably covered in a one-semester course. I have in mind
an audience with prior exposure to the fundamentals of Riemannian geometry and dynamical
systems. I am very grateful for the assistance and criticism of several people in preparing the
text. In particular I wish to thank Leonardo Macarini and Nelson Moller who helped me with the
writing of the first two chapters and the figures. Gonzalo Tomaria caught several errors and
contributed with helpful suggestions. Pablo Spallanzani wrote solutions to several of the
exercises. I have used his solutions to write many of the hints and answers. I also wish to
thank the referee for a very careful reading of the manuscript and for a large number of
comments with corrections and suggestions for improvement.
