There are several types of galaxies: 1. Elliptical galaxies have a spheroid shape with no defined axis of rotation and are classified on a scale from perfectly circular (E0) to flattened (E7). 2. Spiral galaxies have a central bulge, disk, and halo, with older stars in the bulge and spiral arms in the disk. 3. S0 or lenticular galaxies have a bulge and thin disk like a spiral galaxy but no spiral structure. 4. Irregular galaxies have no regular shape and come in two types - Irr I with HII regions and young stars, and Irr II with more dust obscuring stars.