They're 3 independent plays - you needn't see them all to understand the whole story.
Read the Jack O'Brien interview, he sorta explains it.
http://www.lct.org/coast/event_detail_explore.cfm?section=obrien Some quotage:
"JO: Trevor Nunn, who directed it there, was in fact staging the first part while Tom was writing the third. So in point of fact even Tom didn't see it all. No one knew what they had birthed until long after the event was over. Tom said to me two years ago that he was ready to take it back in his own hands and ask the question: What in fact have I created? Yes, it was a trilogy, but it's a curious trilogy because it doesn't have a dramatic arc; it has an historic arc. And, more interestingly, the work is performed by one company. Sometimes characters are sustained and sometimes they are dropped -- somewhat as in Dickens.
...
BL: What is the shaping idea behind the Stoppard trilogy?
JO: Perhaps the most important idea of this play is: Who has the map in history? Where are we? There is no map. When I pulled my personal camera back into a long shot and tried to figure what the hell I was approaching here, I came back to "the coast of utopia,"which is of course Stoppard's title. When you think about that, and you should think about that, utopia is an impossibility. There is no coastline, because you can't get there.
...
BL: How would describe the basic story for people?
JO: This is at first a Chekhovian story and a story that really happened, and a story about a huge wrong that needed to be righted. To put it in fairy-tale terms: Once upon a time, in a country very far away, there were privileged people and great unwashed masses who were hopelessly, hopelessly poor. And some people thought that was not fair. That people shouldn't own people, that people shouldn't measure their wealth in terms of slaves but in terms of enlightenment. And these relentlessly intellectual guys struck flints against an impassive problem until they started a fire. The trouble with fire is, you can't control it. What they tried to do, for the best possible reasons, ended up, in 1917, with murder and cruelty and unbelievable unhappiness. That was the eventuality of revolution, which some people say has to happen. They say that without a revolution of some kind, you can't really effect change.
BL: How do you characterize each play generally?
JO: The first story in many ways is the wittiest, and the most charming, and most romantic, and the prettiest. The second story, gets a little deeper and a little darker. And people die. The third has a kind of intense intellectual brilliance. The trilogy is a marathon, but a very enjoyable one."
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