The Doctor needs somewhere peaceful to recover from his traumatic regeneration. But the sanctuary of Castrovalva is not all it seems, as the Master will stop at nothing to gain his revenge over the Doctor...

After an encounter with the Master, an airline stewardess named Tegan Jovanka becomes an unwitting stowaway aboard the TARDIS as it travels to the planet Logopolis. There, the Doctor discovers that the Master's interference with the Logopolitans' advanced mathematics has unleashed a wave of entropy which threatens to consume the entire universe.

On the planet Alzarius in the alternate universe of E-Space, the Doctor, Romana and K9 find survivors of a crashed starliner, strange creatures lurking in the marshes and a genetic riddle which stretches back centuries.

During World War II, a wealthy Canadian uses his own money to help the Allies form an espionage network.