The video Geodesics and Waves introduces the concepts of straightest geodesics and geodesic flow on polyhedral surfaces. It is the third in a series of videos presenting research results from the area of mathematics and visualization produced at the department of Experimental Mathematics and Visualization at the Sonderforschungsbereich 288 on Differential Geometry and Quantum Physics at the Technical University of Berlin (see [1][2]). Keywords Geodesics, Geodesic Flow, Isometric Texture Maps, Polyhedral Surfaces