Sir Reginald Styles is working into the night to bring together parties from all around the world for a global peace conference. Noticing the curtains fluttering in the wind he goes to close the window and is set upon by a man. Knocked to the floor, Styles is horrified when the man points a gun at him...and then vanishes, like a ghost. The minister is concerned and so UNIT have been asked to investigate. At first the Doctor is not interested but when the Brigadier explains that the world is on the brink of a world war he decides to have a look. Mention of his ghostly attacker intrigues the Doctor further; the discovery of a weapon built with local materials but not of current technology adds further to his curiosity. Jo and the Doctor decide to spend the night at a haunted house - though the Doctor suspects that these ghosts may not be from the past, but from the future.

Once the Doctor and Jo have settled in for the night there is another ghostly visitation. The Doctor is confronted by guerillas from the future: their mission is to kill Sir Reginald Styles. Styles, under the guise of pursuing peace, is in fact about to put the world to the sword and, in the future, the ruined Earth will be taken over by the Daleks.

The planet of Peladon is petitioning to join the Galactif Federation: King Peladin is keen on the idea; Torbis supports him; Hepesh opposes the idea stating that such a course will bring down the Curse of Aggedor upon them. As if to give weight to this, Torbis is attacked and killed by Aggedor, legendary royal beast of Peladon.

Representatives of the Galactic Federation are present on Peladon to consider the petition. Izlyr is the delegate from Mars; there is a delegate from Alpha Centauri; there is a delegate from Arcturus; they are waiting for the Earth delegate - so when the Doctor and Jo arrive, it is assumed that they are the delegates. The Earth delegate is also the chairman delegate: and since only females of royal blood are permitted, Jo is introduced as Princess Jo of TARDIS. Though he is in the role of the chairman, the Doctor knows that he cannot just accept Peladon's petition: there are matters to be considered, including the curse - which appears to cause a statue to topple towards the delegates; some of the delegates are all for leaving Peladon to its old ways and superstitions; the Doctor and Jo believe that they must do all they can to help - but is there truly a curse or is someone trying to sabotage matters? For the Doctor there is only one suspect - the Martian delegates, a foe he has encountered before - he knows them as Ice Warriors.

The Doctor and Jo pay a visit to the Master, imprisoned for his crimes. His cell is the sole occupied cell on an island fortress. Security seems to be up to the job, with guards trained to resist the Master's hypnotic abilities. When the Master seems genuinely repentant, the Doctor is surprised - but not surprised that he will not reveal the location of his TARDIS.

Before the Doctor and Jo return to the mainland they learn of ships that have been attacked in the area recently. Remains of one lifeboat are at a nearby naval base and the Doctor sneaks in to check it out. He is intrigued about the regular pattern of the burn marks on the lifeboat. The sinkings also seem to be near a sea fort which is being renovated. Going out to the sea fort, the Doctor discovers one of the caretakers dead and the other babbling about "sea devils".

On the planet Solos, the natives are being menaced by some strange mutation. Neither the natives nor the humans in the Skybase in orbit around the planet tolerate these mutants. The marshal of the skybase takes pleasure in hunting down these mutants. Solosians have been summoned to a conference on the Skybase: Varan is one of those who agree that the mutants should be hunted and destroyed; Ky believes that the human overlords are responsible for the mutation (in their attempts to alter the atmosphere) and a better solution should be sought. The administrator informs the marshal that Earth is pulling out and will no longer rule over Solos. The marshal feels that Solos should be colonised and that the atmosphere can be made habitable for humans.

The Doctor arrives on Skybase: he has been dispatched there by the Time Lords with a message container. Exactly who the message for is not clear - until Ky escapes from the conference room, fleeing an assassination. The message is for him - but how to get it to him not that he is a hunted fugitive, on a planet with an atmosphere that can only be breathed by the Solosians?

After a nightmare about an eruption, the Doctor asks Jo to keep an eye open for news about eruptions anywhere in the world. Jo is exasperated as she had read out an article to him last night. There is no mention of a trident-shaped crystal though, which the Doctor also saw in his dream. The eruption is in the area of Santorini, believed to be the remains of ancient Atlantis. The Doctor is convinced that there is a definite connection between this and his dream: he contacts the Brigadier and asks him to send out a global alert - for all sections of UNIT to keep a look out for the Master.

The Brigadier and Benton go to the Newton Institute to observe the TOMTIT (transmission of matter through interstitial time) research project. Professor Thascales (the Master) is checking on the data regarding feedback during a TOMTIT experiment run by Dr Ingram and Stuart Hyde: when he discovers that the VIPs attending the demonstration are being accompanied by UNIT he puts on a hazard suit as a disguise, stating that it is a simple precaution as he will be conducting the experiment. The heart of the TOMTIT device is a trident shaped crystal...