"Well, it involves an awful lot of recalculation, and this type's not really my forte." (groan)
IN THIS ONE... The Master reveals himself to the Doctor, he is denied the power of the source, but he still steals Tremas' body.
REVIEW: So the Doctor HADN'T recognized the Master. Those signs of recognition were for the Melkur "as seen on TV". That exposition scene in Part 1 has a lot to answer for. He's being a bit dense not to see it earlier, the materialization sound is a dead giveaway. With the power of the Source at his command, the Master becomes a pretty powerful telekinetic. His black-paneled TARDIS makes a change from the way he used to slum it in the Doctor's set. And the new make-up, theatrical though it is, is a lot more mobile than the rubber mask from The Deadly Assassin. No, he'll never be Roger Delgado again, but if Beevers had been allowed to rejuvenate as himself, I think I would have been very happy with a new Master traipsing around the universe (and I say this on the strength of the Big Finish audios he would later star in). Denied the power of the Keeper by the heroes' intervention, he's forced to steal Tremas' body instead (don't name your kids with anagrams of the word Master if you don't want this to happen to them), and with all due respect to Anthony Ainley, I've always found his Master way over the top (the scripts didn't help, of course). Thematically, it accomplishes the final corruption of Tremas, which the Master was always working at in a way, worming his way into his family through Kassia, and in this episode, forcing him to shoot Neman. As for the Master being a body snatcher now... see Theories.
Even as the Master gains new magical powers, the episode works hard to de-mythify the TARDIS, to what possible end, I don't know. The Master's own TARDIS is set up like a regular spaceship, with a console on the wall in front of the scanner(s). And not only does Adric seem quite capable of puttering around the TARDIS' innards, but soon enough, Nyssa's doing it too! It's like Time Lord technology is pretty much like any other, and can be cannibalized for parts to make whatever [TECHNOBABBLE] gadget your need to resolve the plot. And this is very much how this particular plot is resolved. Adric and Nyssa talk tech nonsense while working at a console, while the Doctor and Tremas talk tech nonsense while working at another. Throw up a big wind at the end to make flipping switches harder all you want, it's still a climax where the heroes flip switches on machinery we can't hope to understand.
The ending is rather sketchy, in fact. The Doctor escapes the Master's TARDIS by jumping through a pane of glass(?). At a crucial moment, the consul "without greatness in him" jumps in the Keeper's chair so the Union can survive (well... see Logopolis, coming up next). And it's quick goodbyes for the Doctor and Adric. That's the second new companion in a row who isn't seen boarding the TARDIS at the end of their first story. But we need Nyssa to walk around the sets calling to her father, now lost and integrated into the Master. On first viewing, it doesn't appear she'll ever become a member of the crew. It's just another scene in the final irony of the Doctor saying it would be nice to always be right, as if he'd been right this time, when in reality, he took off before the Master was actually defeated, with tragic consequences for the new friends he leaves behind.
THEORIES: So what's going on with the Master snatching bodies? In The Deadly Assassin, he wanted to use the Eye of Harmony's great energies to renew his crispy undead self. In The Keeper of Traken, he has a similar plan predicted on getting access to the Source. In this case, he believes that power will allow him to steal the Doctor's body and thus get access to all those unused regenerations. Denied that opportunity, he settles for Tremas' single life, though merging with him does make him a younger man (with a slightly different outfit). How? We know he absorbed some of the Source's energy, which is no doubt what powered the trick, but as neither Time Lords nor the Keeper seem to normally have access to such a trick... It's probable that a Time Lord's cells have the potential for transformation. After all, they're expected to change form twelve times in their lifetimes, and while DNA seems more mutable in the Whoniverse than in our own generally, it can help explain some of the stranger transformations the Doctor undergoes from time to time (ex.: The Two Doctors, Last of the Time Lords). Among the Keeper's abilities is, I suppose, a sort of omnipresence across the Traken Union. If he can be anywhere, or at least transport himself anywhere, what if he moved inside you. The Time Lord cells graft onto your own and voilà! Body-snatched! It's even possible the trick can only be achieved because Trakenites have some affinity with Time Lords - a peaceful but decaying society, great science and intellect, and their own Matrix-like network. But this is all conjecture. All we really need to know is that the Master is a survivor. He's probably collected skills and gadgets from across space and time to keep himself alive.
VERSIONS: There are no important differences between the televised program and the Target novelization that I am aware of.
REWATCHABILITY: Medium - Some important happenings, but ultimately, the climax is only about pushing buttons.
STORY REWATCHABILITY: Medium-High - For entertainment value, The Keeper of Traken is just a Medium. Generally good actors in generally pretty sets, some cool twists and turns too, but with an unsatisfying climax. Historically, it gets an extra point because it introduces Nyssa and the new Master, which may make it required viewing.