Tom Baker's final story as the Doctor, and debut of Janet Fieldings appearance as Tegan The Doctor takes Adric and a young air hostess named Tegan Jovanka, who has come aboard the TARDIS by accident, to the planet Logopolis, home of a race of mathematicians whose help he hopes to enlist in reconfiguring the outer shell of the TARDIS.

The mysterious, wraith-like Watcher brings Nyssa from Traken to join them and warns of impending danger - something that is borne out as the Master arrives and kills a number of the Logopolitans.