The wizard Drum Billet knows that he will soon die and travels to a place where an eighth son of an eighth son is about to be born. Since such a boy is destined to become a wizard (on the Discworld, the number eight has many of the magical properties that are ascribed to seven in the real world), Billet wants to pass his staff on to him as his successor.  However, the child born is actually a girl, Esk (full name Eskarina Smith). Since Billet notices his mistake too late, the staff is passed on to her.  As she grows up, it becomes apparent that she has uncontrollable powers, and the local witch Granny Weatherwax decides to travel with her to the Unseen University in Ankh-Morpork - but a female wizard is something completely unheard of on the Discworld.  Esk is unsuccessful in her first, direct, attempt to gain entry to the University, but Granny Weatherwax finds another way in; as a servant. While there she follows the progress of an apprentice wizard named Simon, who she had met earlier, on her way to Ankh-Morpork. Simon is a natural talent (wrongly referred to as a sourceror) who invents a whole new way of looking at the universe that reduces it to component numbers. His magic, however, is so powerful that it causes a hole to be opened into the dungeon dimensions. With Eskarina's help Simon discovers the weakness of the creatures from the dungeon dimensions, and manages to transport both himself and Eskarina back into the Discworld.