This graduate course provides a quantitative look at several visual transformations that were covered qualitatively in the prerequisite course Sensation and Perception. It is fairly mathematical, involving systems theory, network theory, machine learning, differential geometry and other formal structures. As always I do not assume students know any of the math, but rather teach it, emphasizing concepts and not useless details. The thinking is not that students will become vision researchers and eventually use the mathematics I teach, but that they will benefit from understanding that mathematics is not so much a tool for analyzing computational systems as it is a discussion in the natural language of the system. For example, there is no way to understand what retinal neurons do with an image without understanding the basic principles of convolution (see figure).