The Mule has successfully conquered the First Foundation, without much effore really.  An event Hari Seldon's plan didn't predict at all.  But if the Mule wants to rul the entire universe, he has to find and conquer the Second Foundation as well, and that other Foundation is very discrete about its existence, let alone about its location.  Han Pritcher, now general, and Bail Channis are sent out on an expedition to find that Second Foundation.  A few vague clues is all they have; there cannot be many people in the Second Foundation, and the two Foundations are at "opposite ends of the Universe", that's almost all there is to find.  And Ebling Mis' surprise when he found out where the Second Foundation was, seconds before he was killed (see Foundation and Empire) could be seen as one of those vague clues.  And another of those vague clues is that the expedition seems to be a dangerous combination of betrayal upon deception.  But who's betraying who?

Years later the Mule is no longer there, and the First Foundation returned to "business as usual".  Which means expanding its reach through trade mostly, and also wondering about the Second Foundation.  Now that rumour has it that it was the Second Foundation that managed to "adjust" the Mule, despite the Mule's enormous powers, the Second Foundation is seen as a threat, and has to be found and defeated.  A group of scientists thinks they have found a way to discover this Second Foundation, and they carefully plan an expedition.  Unfortunately the stubborn fourteen year old Arcady has a mind of her own, and as a stowaway she starts a trip which will bring her closer to the truth than anyone could have imagined.

This is the third and final book of the original trilogy, which means that the story is sort of wrapped up.  Still there are enough loose ends left to explore, and that is what will happen, be it decades later.  Now that it's wrapped up it shows that this trilogy is not like "traditional" trilogies, where in the first book we meet the characters and see the trouble they're in, in the second that trouble deepens, and in the third they solve the problems.  In a way any trilogy is utterly predictable - think of Lord of the Rings, where you know right from the start the Ring has to and will be destroyed - but the Foundation trilogy is different.  Yes, there is a winner in the end, but not the one you expected.  Yes, there was trouble in the middle (the Mule), but not of the kind you expected.  No, there is not one hero, there are several, but none of them are carrying the whole story.  If something is carrying the story it is a science, "Psychohistory".

Asimov isn't the kind of author that brings to life incredibly rich societies with all kinds of environments and creatures that interact and work towards the resolution.  In stead his stories follow an irrefutable logic, a logic that leads the reader to believe that only one outcome is possible.  And then things happen that show that Asimov gaves his stories and how they fit together much more thought than the reader assumed at first.  This book is not different.