The Long Earth Series
The Long Earth Series is a collection of science fiction novels collaboratively written by Terry Pratchett and Stephen Baxter. The central premise is that there are a series of parrallel Uiverses that are just one small step away from each other. Each of these Universes are a carbon copy of ours but with variations. A device known as a Stepper allows travel between these places. A few individuals have a natural ability to step without the need for any device.
The one major difference is that our Earth (Known as Datum Earth) is the only one that is inhabited by humanity - specifically Homo sapiens. The novels follow the events following Step Day after these parrallel Universes are first discovered.
The series is currently scheduled to contain 5 novels, with three currently published.