Having demonstrated the existence of external galaxies, Edwin Hubble undertook the task of classifying galaxies according to their shape and appearance. The results of his work are now known as the Hubble Classification Scheme, and it continues to be widely used in astronomy today. Hubble defined three main classes, elliptical galaxies, spiral galaxies, and irregular galaxies. There are subgroups in all these catagories.
Figure: The Hubble galaxy classifications, arranged in the traditional "tuning fork" pattern.