The Long Earth, by Terry Pratchett and Stephen Baxter
Discover of the long earth begins when kids in Madison, Wisconsin start building a simple electrical device powered by a potato. When they flip a switch, most of them disappear, reappearing in a forest, confused and nauseated. Orphaned teen Joshua helps bring the children home. They had stepped into one of thousands of parallel Earths. Soon, pioneer colonists and entrepreneurs settle in nearby Earths, hampered by the fact that iron can’t cross the border. Some people can’t step, either, and this creates resentment. Governments and police struggle to keep up with all of the changes.
Fifteen years later, Joshua is approached by the transEarth Institute. A Tibetan mechanic reincarnated as an artificial intelligence wants Joshua to travel with him in an airship to distant Earths. They travel quickly, as Joshua is a natural stepper who experiences no nausea and doesn’t even need a device. They encounter varied settlements, exotic and sometimes dangerous fauna, and varying geology and climates. They meet Sally, the daughter of the device’s inventor. Other, more primitive, hominids are found, and some of them are fleeing from danger towards main Earth, where the anti-stepping crowd is becoming more vocal. A strange and marvelous journey, with some of Pratchett’s usual humor.