Anosov Geodesic Flows on Surfaces

This paper is an exposition of the major results of P. Eberlein’s paper, “When is a geodesic flow of Anosov type? I,” in the special case when the manifold $M$ is a surface. We follow Eberlein’s coverage closely, adding details when helpful, and taking advantage of simplifications given by the dimension two case. The objective is to give readers a more tractable introduction to the important topic of Anosov geodesic flows, which highlights key concepts and arguments without worrying about generalizations to arbitrary dimension.