1985 Philip Jose Farmer
Part of Farmer's genius is starting with a truly imaginative premise. You can see this in his other works like Riverworld. Start with a compelling premise, and from there, the story just flows. In this case he imagines a world where overpopulation is such that the average person is active only one day out of the week, spending the other six in suspended animation, during which other people take their day until next week comes around and it is his day again.
So, one person might be a 'monday' and every monday he comes out of his stasis capsule, lives his life, then returns to the capsule promptly at midnight. A few minutes later, all the 'tuesdays' come out and so on. Humorously, Farmer refers to the suspended animation as being 'stoned' - as in molecules slowing down to the consistency of stone - and the capsules as 'stoners', so of course I have a little chuckle everytime I read a sentence referring to someone as being stoned.
This system is of course implemented and enforced by the gub'mint, ostensibly for reasons of resource shortage and overpopulation but of course there is the real, hidden reason as well. Not adhering to this is a serious crime, and being caught on a day that is not yours -daybreaking-without a temporal passport is bad news. So of course one man bucks the system, and instead of returning to his stoner every night, he goes from one day to the next, with a different identity and a different life (and a different wife!) every day of the week. His life as a daybreaker is the focus of the book.
This premise has all sorts of interesting conclusions that follow. Since these citizens are only active one day out of every 7, this affects the calendar. Time as we know it is objective time, called obweeks, obmonths, obyears, etc. Time to these people is subjective, so one week to them looks like a line drawn vertically through 7 mondays on a calendar, called one subjective week or a subweek. So in theory a citizen may live 50 subyears which in real time is 350 years. Furthermore, since everyday consists of a different pool of persons actively living, different trends, cultures and societal norms arise, though all share the same resources and living space etc.
The premise would be nothing without a story, and luckily Farmer delivers this as well. The protagonist's need to maintain seven separate identities means he gradually develops a dissociative identity disorder and Farmer superbly explores this effect, as well as weaving a compelling plot revolving around secret societies and government conspiracies against this highly original setting.
This idea was first developed by Farmer in the short story "The Sliced-Crossways Only-on-Tuesday World" some years before the publication of Dayworld. It's a great short story, which you can read here