This thesis deals with the propagation of spin waves in thin Ni80Fe20 films. Its specific aims are to experimentally determine a dispersion relation for propagating spin waves in thin ferromagnetic films, and to determine phase velocities, group velocities and damping. Additonally, an analytic dispersion relation based upon the linearized Landau-Lifshitz-Gilbert (LLG) equation is derived, from which the experimental findings can be reproduced using a theoretical model. Further on, this thesis reports on the direct observation of the interference of spin waves. This thesis is structured as follows: After an introduction in chapter 1, the basic principles of magnetostatics are sketched in chapter 2, followed by the principles of magnetodynamics in chapter 3. Based upon these principles, in chapter 4 a theory for the propagation of spin waves in ferromagnetic thin films is developed. The experimental part of this thesis begins with an overview of the experimental setup for Time Resolved Scanning Kerr Microscopy (TRSKEM) in chapter 5, and continues with the results of spin wave propagation and interference in chapter 6. The experimental results are compared to the theoretical predictions of the model developed in chapter 4. Chapter 7 gives a summary of the results and an outlook towards possible future developments. The appendix gives additional information on experimental and theoretical details.