The Long Earth, The Long War, The Long Mars, The Long Utopia, and The Long Cosmos, by Terry Pratchett and Stephen Baxter. This is in some ways a very odd series - bit in content, but in structure. It really needs an omnibus, because although it’s published in five volumes, it’s as much a single story as Lord of the Rings. Most of the volumes end on cliffhangers, or just stop. But taken as a whole, it’s pretty darned good and periodically excellent.
The story begins on the day people around the world first use homemade devices to cross between parallel worlds. With the Stepping Box, each step carries you to the next world “east” or “west” of the world you were in, minus any iron objects you were carrying this makes most people very nauseous for a few minutes, but there are ways to fix that, and it’s possible to step quite rapidly. East and west are notional terms - the Long Earth is a possibly infinite line of alternate worlds fixed in relation to each other.
There are interesting features to the setup. One (1) world has humans on it. Others for quite a long way, hundreds of thousands of worlds in either direction - don’t have sentient life. Farther away, there are descendants of various of the hominids our ancestors shared the planet with. Each world generally has just about the same history as the ones adjacent to it, and there are “belts” sharing overall climate and major developments. Datum Earth is part of a belt of worlds in the midst of an interglacial moment, for instance. Farther away, you can find belts of warm spells not in the midst of a glacial epoch, where one or another mass extinction didn’t happen, where the Yellowstone supervolcano has already exploded, even a few where as astronomical calamity obliterated the Earth. (You can step past the resulting gap, one step in, one out, but you have to be prepared for the moment of vacuum and weightlessness.) and so on.
Among other things, this would be a ridiculously gamable setup.
The five books take us from Stepping Day though most of the century. The scope zooms out from Madison, WI to millions of steps away in various parts of the worlds, though crises including terrorism, vulcanism, imperialism, and secession, to the exploration of Mars’ alternates, to first contact of a sort and what comes of it. As befits the collaborator, there is persistent optimism but also reasonable share of drama and tragedy. There children and grandchildren of some early characters around at the climax.
Good stuff once you take th structural oddness on board.