The Book: Foundation by Isaac Asimov. Originally published by Gnome Press in 1951, the edition read was published by Avon in 1966 or so.
The Setting: Some really distant planets. Trantor, Terminus, others.
The Story: Humans really kicked some ass in the Universe. But stuff is gonna fall apart. One guy can see that (mathematically), and creates a situation which will help to make the Intergalactic Dark Ages suck a lot less.
The Science: The obvious idea to focus on is that of psychohistory. That by applying history, sociology, and mathematics to societies, one can statistically predict the future. It is an awesome foundation for these stories. But I don’t think anyone is going to come along who can map out the next 1000 years of the human race with any sort of accuracy. It’s not really plausible. But it’s plausible enough to buy into totally.
The Reaction: Loved it. Loved it. Wanted more. Wanted lots and lots more. Great stories, great writing. There’s a reason this is a classic of the genre and other-books-I-could-mention-but-won’t-because-you-can-just-scroll-down-a-ways aren’t.
The Cover: No cover art credit. I’m not a fan. It’s the cover art I associate with these books, but it’s kind of dull. Though it does succeed in being enigmatic and probably highly symbolic, though I’m not paying that much attention because I’m bored already.
Next Up: Stowaway to Mars by John Wyndham