This final book in Asimov's Foundation Trilogy is essentially a high-tech tale of hide-and-go-seek. It recounts the story of a band of fellows from the First Foundation attempting to find the location of the Second Foundation, and the Second Foundation attempting to remain hidden. Way back in the first book of the trilogy, a man named Hari Selden founded the Foundation as a means to maintain scientific know-how amid a crumbling empire so that civilization goes into the dark ages for a few hundred years rather than a few thousand. The Foundation is founded around men with a lot of physical scientific knowledge. Selden, himself, was a mathematician, but he used it to create sets of probabilities that could predict the future, and as becomes clear by the second book in the series, to control people's minds.
That there is a Second Foundation on the opposite side of the galaxy is a myth or rumor that has long existed. This Second Foundation, the rumor goes, belongs to people who can control minds and predict the future but who do not have any technical know-how.
A band of fellows come to the conclusion that such a foundation exists and decide that they must discover and destroy it so that the First Foundation will not falter.
Meanwhile, the Second Foundation is worried. It's worried because the future that has been foretold has been messed up by an individual. As a result, the probability that the galaxy will descend into complete chaos has risen to heights that demand action.
Since readers know that there is a Second Foundation, the book is intriguing mostly because readers don't know the actual location of the Second Foundation. Like the First Foundationers in search of it, readers move forward with excitement to see if the place where this foundation exist will ever be found. Asimov throws a number of twist endings in toward the last few chapters, as the First Foundationers reach various conclusions: that the Foundation doesn't exist, that it does and it's scattered or all among us, and so on. Each option seems plausible. But readers are in on an irony that the poor First Foundationers are not.
If the trilogy is seen as an exploration of fate versus choice, Asimov's answer seems to come down slightly in favor of fate. But to say that he wholly embraces fate would be difficult. After all, the probabilities, once the appearance of the Mule occurs in book 2, are stacked against what Selden had predicted mathematically, so to keep such events in line, they must be perennially fine-tuned by a set of men who pull strings. If so, then someone somewhere pulling the strings still have free choice, even if those being pulled along do not.