What happens if two galaxies collide? The average distance between bright galaxies is only about 20 times their size, so over the history of the Universe (14 Billion years), we expect that most bright galaxies will have had at least one close gravitational encounter with a neighboring galaxy. This lecture explores what happens when two galaxies undergo interactions ranging from passing tidal interactions to head-on collisions, all the way to multiple collisions and galaxy "cannibalism" in the centers of large clusters. While at first glance galaxy interactions explain rare "peculiar" galaxies, on closer examination we find that galaxy interactions and mergers are central to understanding the assembly and evolution of galaxies. At the end, we take a speculative look at the distant future 3-4 Billions years hence if in fact Andromeda and the Milky Way are on a collision course. Recorded 2006 February 15 in 1008 Evans Laboratory on the Columbus campus of The Ohio State University.