Here is a recent, detailed, comprehensive overview about the range of galaxy morphologies found in our universe and about how galaxies are classified. The author, Ron Buta, is a very expert galaxy classifier, though it deserves comment that nearly all of his scientific output has been about galaxies with prominent disk structures (Spiral Galaxies and S0 galaxies), so a specialist in elliptical galaxies (spheroids and halos and bulges) would give a different emphasis.
http://carina.fcaglp.unlp.edu.ar/ext...Morphology.pdf
( If you have a look at his "The de Vaucouleurs Atlas of Galaxies, you will find little about the classification and nature of bulges and spheroids, but a lot about disk phenomena.)
This review paper is in "Planets, Stars, and Stellar Systems, Volume 6"(2011)