The first thing that strikes you about The Invasion of Time is how fast it moves. (Well, all right, maybe not the first thing, but close.) This story flies in comparison to Underworld: we move from the Doctor forming an unholy alliance of some sort to being inaugurated as President in the space of 24 minutes.
That alliance is also particularly intriguing, as it seems to set up the Doctor as the villain of the piece. "You promised complete control over the Time Lords," he says to the mysterious party he's meeting with. "... I'm honoured to be allowed to serve your glorious cause." And from this moment on, the Doctor is behaving distinctly erratically, with sudden mood swings from friendly to near-apoplectic to deadly calm. He refuses to let anyone know what's going on, preferring instead to boss everyone around as he demands to be installed as the President of the Supreme Council of the Time Lords (being, at the end of The Deadly Assassin, the only viable candidate remaining). It's a fascinating approach -- we know the Doctor must be up to something (right?), we just don't have any idea what. It certainly looks like he's planning to betray the Time Lords...
The Invasion of Time is one of those rare things in early Doctor Who: a loose sequel to an earlier story (The Deadly Assassin -- but you already knew that). Of course, other than using events from The Deadly Assassin as a jumping-off point, there's not too much overt sequelness on display: some of the sets look similar (even if they're lit significantly differently), and Borusa is back (albeit as a different actor), and there's some reference to the Matrix. And that's about it. It's slightly surprising that they didn't try to get any of the actors from the earlier story back (well, they apparently did try to get Angus Mackay back as Borusa, but he was busy), as it might have made the connections stronger.
But that's okay. These first two episodes are ultimately Tom Baker's, and while there is the occasional misstep (such as the infamous "even the sonic screwdriver won't get me out of this one" line, which Baker delivers to the audience), for the most part he excels, continually wrongfooting the audience as to his motives and holding us entranced with his performance. That uncertainty as to his motives also keeps things moving, and moments such as the one where he discusses with K-9 the probability of his plan succeeding, which almost look like it could go either way as to his loyalties, go a long way in maintaining interest.
Plus, episode two features one of the all-time best cliffhangers (and my personal favorite) in the entire series: after K-9 destroys the barriers that keep Gallifrey isolated from the universe, the Doctor calls a meeting of the High Council. "Gentlemen, this is no ordinary meeting," he declares. "I'm privileged to introduce to you your new masters." And as odd-looking shimmering shapes appear, we see the Doctor laughing evilly, and we really start to wonder just what is going on. Has the Doctor really become a villain? You really want to tune in next time to find out.