Talk to Raminus to receive the quest for promotion to Magician. He will ask you to acquire some information regarding Black Soul Gems from Tar-Meena. Find Tar-Meena in the Mystic Archives, ask her about Black Soul Gems, and she will tell you to locate a book called Necromancer’s Moon. You can find the book on a small table on the lower floor of the Library. Return to Tar-Meena with the book and she will give you some information about the book and send you back to Raminus.
Raminus will respond by sending you to talk to Bothiel. She doesn’t help you much, but she does give you a note, listing several locations, left by Falcar who was also interested in Black Soul Gems. Talk to Raminus again and he will send you to Dark Fissure Cave, south of Cheydinhal to learn more. To complete the quest, all you technically have to do is enter the cave, kill the Anchorite Worm on the left as you enter, and take the Handwritten Note from his body. Take the note back Raminus and speak to him about Advancement to receive your promotion to Magician.