I'm currently buzz-sawing my way through the seven books in Asimov's classic Foundation series. I read the original Hugo-winning three books - Foundation; Foundation and Empire; and Second Foundation - many years ago, and didn't realize that additional books had been added to fill in the gaps, so I decided to go back through the entire collection chronologically (to the story, not in the order published).
The series chronicles the fall of the Galactic Empire, in the distant future, after twelve thousand years of domination, and Professor Hari Seldon's prediction of the collapse using the field he created called Psychohistory, which is a form of mathematics that allows the prediction of general changes across worlds and the galaxy. Psychohistory also provides the foreknowledge to shorten the anarchy subsequent to the collapse by a factor of thirty, from thirty thousand years to only one thousand years.
Seldon uses his knowledge to create two "Foundations", which will serve to replace the Galactic Empire after the fall. One Foundation is tasked with documenting all of human knowledge so that it will not be lost in the anarchic period. The Second Foundation is comprised of humans with special mind powers, including Seldon's granddaughter, who are to combine their powers to create a sort of "universal consciousness" to benefit humankind.
After several future "Seldon crises", as they are called, the two Foundations eventually confront each other to determine which will actually end up being the core of a new empire. Along the way there are confrontations with the dying Empire and a mysterious mentalic called "The Mule". And the series concludes with the rediscovery of Earth, the origin of human life, which has mostly been forgotten over the millennia and is thought to be only a myth.
In going through the books, I am glad to see some of the gaps filled in, especially the history of Hari Seldon, although there is a lack of continuity in several places. If you are willing to ignore these inconsistencies, though, you'll find a very entertaining classic science fiction story by one of the masters of the genre.