  It is well-known that hyperbolic flows admit Markov partitions of arbitrarily
small size. However, the constructions of Markov partitions for general
hyperbolic flows are very abstract and not easy to understand. To establish a
more detailed understanding of Markov partitions, in this paper we consider the
geodesic flow on Riemann surfaces of constant negative curvature. We provide a
rigorous construction of Markov partitions for this hyperbolic flow with
explicit forms of rectangles and local cross sections. The local product
structure is also calculated in detail.
