Fossil galaxy groups, fossil groups, or fossil clusters are believed to be the end-result of galaxy merging within a normal galaxy group, leaving behind the X-ray halo. Galaxies within a group interact and merge. The physical process behind this galaxy-galaxy merger is dynamical friction. The time-scales for dynamical friction on luminous (or L*) galaxies suggest that fossil groups are old, undisturbed systems that have seen little infall of L* galaxies since their initial collapse. Fossil groups are thus an important laboratory for studying the formation and evolution of galaxies and the intragroup medium in an isolated system.