Geodesic and Horocyclic Trajectories presents an introduction to the topological dynamics of
two classical flows associated with surfaces of curvature -1 namely the geodesic and horocycle
flows. Written primarily with the idea of highlighting in a relatively elementary framework
the existence of gateways between some mathematical fields and the advantages of using them
historical aspects of this field are not addressed and most of the references are reserved
until the end of each chapter in the Comments section. Topics within the text cover geometry
and examples of Fuchsian groups topological dynamics of the geodesic flow Schottky groups
the Lorentzian point of view and Trajectories and Diophantine approximations.
