While the Doctor and Romana desperately rack their brains over how to escape E-Space, Time Winds strike the TARDIS, damaging it and K-9. Strangest of all, it allows Biroc, a hurt and hunted lion-man, to enter, phased in time, and set the control coordinates at zero-zero, sending the TARDIS into a milk-white void. Before running off, he warns of others who will be soon following.
Three humorless men from a damaged bulk freighter find the TARDIS. Wearily, Romana returns with them to appraise the situation of their damaged ship but, because she's a time sensitive, winds up as a living navigational component to replace their time-sensitive Tharil (lion-man) who escaped. Meanwhile the Doctor, having found a gateway, is having a time with Gundans, robot soldiers programmed to kill.
While Biroc leads the Doctor to a view of the Tharil's lordly past, Romana learns more about the damaged freighter and the coldheartedness of its crew. Meanwhile Commander Rorvik, confounded by the time mirror inside the universal center gateway, ignores evidence that it's no simple mirror and decides to blast it, imperiling the lives of everyone.
Returning to N-Space, The Doctor and Adric are summoned to Traken, a planet of peace and harmony. The Keeper of Traken is nearing the end of his 1000-year-old reign and one of the Traken consuls is to become the next Keeper. The Doctor, Adric, Tremas (the Keeper Nominate) and Nyssa (his daughter) set about to stop the Melkur, a calcified figure believed to be a "Source of Evil" trying to destroy the Traken Union, only to later discover it is the guise of a old enemy of the Doctor - The Master - who plans to take control of The Source (the keystone of Union) so he can ...
Tremas claims counselor privilege to protect the Doctor and Adric from execution, though it binds his fate to theirs if they're found guilty of murder. Melkur strengthens his hold over Kassia while Seron decides to have rapport with The Keeper to learn truth, and Adric finds evidence of another TARDIS in the area.
With Tremas falling under suspicion, due to his association with the Doctor, a new Keeper Nominate is named. Now, with everything in place, Melkur has only a short wait before his full malevolence can unfold.
Preparing to overhaul his TARDIS, the Doctor goes to Earth to take fresh measurements of a police box. A figure in white observes, as the Master lies in wait with a puzzling predicament for his rival Time Lord.
With the threat of doom ever-present, the Doctor and Adric press on for Logopolis, where the muttered mathematical incantations of its people can completely overhaul the TARDIS. En route they discover an accidental yet demanding passenger on board while, all the while, the Master secretively journeys with them to ensnare the Doctor in a diabolical trap.
With Nyssa from Traken unexpectedly rejoining the group, Adric aids the Monitor of Logopolis in trying to save the Doctor before time runs out. The Master, at liberty to prepare, is finally ready to reveal his true target, which unknowingly sets off the biggest catastrophe of all time.
With the universe collapsing, the Doctor forms an uneasy alliance with the Master to save it. In case all does not go well, the Watcher takes the Doctor's companions to a safe place, but his plans for them don't stop there. The one hope for all lies back on Earth.