The story revolves around the planet Shada, on which the Time Lords have constructed a high security prison for some of the Universe's most dangerous criminals. Skagra, a flawed genius from the planet Dronoid, wishes to create a "Universal Mind" in which all the pooled knowledge of the universe's greatest criminals would be placed at his disposal and with which he intends to take control of the Universe. Skagra wants to go to Shada to extract the knowledge of the criminals who have been imprisoned there. Unfortunately for Skagra, knowledge of the location of Shada has been deliberately hidden by the Time Lords, but Skagra discovers that there is a Time Lord living on Earth in the twentieth century who may hold the key to its location. This Time Lord is masquerading as a professor at St. Cedd's College, Cambridge and calling himself Professor Chronotis. Sensing danger, Chronotis calls for the assistance of his old friend and protégé, the Doctor. The story climaxes in a battle for control of the Universal Mind.