The Man in the High Castle
The Man in the High Castle, by Philip K. Dick
I've had an old paperback library copy of this on my TBR pile for quite a long time. I don't know if anyone wrote any alternate-universe books about a different outcome to World War II before Dick did, but this is the most famous one. It's the late 60's, and the Axis won the war. Japan occupies the West Coast of the American continent and Germany owns the East Coast as well as all of Europe and Africa. Africa has been depopulated, black people are mostly enslaved, Jews live in hiding, and everything is very racialized. White people in California live in subservience to the Japanese (as do the Chinese). And Germans are sending rockets out to colonize the solar system, too. Although Japan and Germany are officially friendly, the cracks are starting to show.
The action mainly takes place in San Francisco or the Midwest (which is the only remnant of the USA and mostly ignored), and jumps between several main characters. An influential Japanese businessman, a Jewish craftsman passing as Aryan and his estranged wife, an antiques dealer, a German trying to warn Japan of imminent attack--all of them are trying to survive. Then there's a book circulating around about an alternate universe in which the Axis lost the war...but it's not our version of what happened.
Anyway, the ending is strange. Funny, but for an SF classic it's not exactly very heavy on the science fiction. It's worth reading, though, if you're interested in alternate histories or SF classics. I'm counting this as my SF requirement for Mixing It Up, too.