In this report we extend the ideas behind classical multiscale signal processing techniques in order to analyze data residing on graphs. In particular, we extend the notions of filtering, downsampling, and upsampling to functions defined on graphs. We then use these notions to define a Laplacian pyramid scheme that generates a multiscale transform for signals on graphs. Possible applications of our proposed transform include coding, denoising, and function recovery which are among the most important tasks in signal processing.