Is there a read about soul gems, possibly "All about Soul Gems"?
What is the use of their various types, and what makes the "black" one outstanding?

Soul gems come in six types. Five normal are: petty, lesser, common, greater, grand. These ones can hold the souls of creatures.

Black soul gems are equal in power to grand soul gems, but are the only type that can hold npc souls. The npc types are the bandits, necromancers, markers, dremora. Be aware that black soul gems will also hold creature souls if there are no suitable soul gems in your inventory.

Azura's star is the equivalent of a grand soul gem, and cannot be destroyed. It cannot hold npc souls however.

I hope this helps you.

Yes: http://www.uesp.net/wiki/Oblivion:Soul_Gem

Make sure and follow the sub links therein to learn even more.

Thank you, UESP appears to be an exhaustive source for many questions!

There's also a book in the game that slightly touches on the subject, lore wise. http://www.uesp.net/wiki/Oblivion:Souls,_Black_and_White.