A series of four science fiction novels written by James Blish in the years 1955 through 1962.
Blish conceived these the old fashioned way: "Given a particular technological advance, what would happen?" The "advance" in this case is a well-handwaved but ill-named means of propulsion called a "spindizzy", which works best on really big things, like for example cities uprooted intact along with a layer of bedrock for cohesion. Okay! Really Big Things flying through space! Science Fiction! Vast, coruscating energies! Exploding suns! White-knuckled high adventure in the far reaches of far galaxies! Right?! Well, kinda sorta. Maybe.
E.E. "Doc" Smith could've gone somewhere with it. Blish didn't.
The whole mess proceeds as follows:
They Shall Have Stars, wherein everybody leaves Earth;
A Life for the Stars, wherein everybody wanders around for many centuries;
Earthman, Come Home, wherein the hoary SF convention of colonies returning to destroy the home planet is ponderously reiterated;
The Triumph of Time, wherein the author emits an ocean of pseudomystical gobbledygook in an ill-advised attempt to Tie the Whole Thing Together and make it all mean something -- and not just any old something either, but something, like, really deep.
Like many "hard science fiction" authors (not that he was one), Blish had crippling literary shortcomings, but unlike Niven or Clarke he didn't have much science or imagination to fall back on. I seem to recall that he spent the last years of his life writing for television: A fitting end.
Of course, I did stick with it all the way through. It's not unreadable.
Dhericean notes the following: "Cities in Flight is also commonly referred to as the Okie Series (which ISFDB catalogs it under). Also development of anti-agathic [anti-aging] drugs is important to the story. The series was inspired by John W. Campbell feedback to a short story." -- But to go into detail on that would be enough material for another whole writeup, which I've asked Dhericean to add.