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The Foundation Series is a science fiction series by Isaac Asimov. There are seven volumes in the Foundation Series proper, which in its in-universe chronological order are Prelude to Foundation, Forward the Foundation, Foundation, Foundation and Empire, Second Foundation, Foundation's Edge, and Foundation and Earth.
The premise of the series is that mathematician Hari Seldon spent his life developing a branch of mathematics known as psychohistory, a concept of mathematical sociology (analogous to mathematical physics). Using the laws of mass action, it can predict the future, but only on a large scale; it is error-prone on a small scale. It works on the principle that the behaviour of a mass of people is predictable if the quantity of this mass is very large (equal to the population of the galaxy, which has a population of quadrillions of humans, inhabiting millions of star systems). The larger the number, the more predictable is the future....(click on the link above for more, or just read the books)
.The Mule was a person who didn't fit into the mathematical model: a mutant of the species with extraordinary abilities, and behavior.