Written in 2005, Moscow, Rough Draft by Sergey Lukyanenko is a science fiction novel of the "parallel world" genre.
Kirill, a Russian living in Moscow, one day discovers that he has the ability to go to other worlds parallel to our Earth.
Everybody forgets him (even his parents and dog), another person lives in his apartment, all IDs and files in all offices disappear.
After a while Kirill meets a special group of functionals, so called because they gained supernatural abilities making them excellent in some profession.
Kirill also encounters an underground, that is, a few people fighting against the 'corporate laws' of functionals and their working for themselves or the elites of other worlds.
Those nicknames are not always consistent - for example, functions and their allies tend to refer to Earth 3 by the name of a city-state that's closest to the watchtower they use to get there.