Do galaxies move?

Yes, galaxies do move. They both rotate and move through space. Galaxies rotate around their centers with the sections of the galaxy that are farther out from the galaxy's center rotating more slowly than the material closer to the center. Galaxies are also moving away from each other due to the expansion of the Universe brought on by the Big Bang. A galaxy which is part of a group of galaxies, called a cluster, also rotates around the center of mass of the cluster.