There are three main types of galaxies: spiral galaxies which have spiral arms radiating from a central core, elliptical galaxies which are spherical or oval in shape, and irregular galaxies which have no defined shape and may exhibit unusual features like radio emissions or gas jets. The document provides examples of each type of galaxy including the Andromeda Galaxy and Milky Way as spiral galaxies, M100 as an elliptical galaxy, and the Magellanic Clouds and Antennae Galaxies as irregular galaxies.