The World of Tiers — Philip Jose Farmer

The Tiers series chronicles the adventures of both Robert Wolff, a man from our world transported through space-time to a cosmos with dimensions and laws different from our own, and Kickaha the Trickster (a.k.a. Paul J. Finnegan, also from our contemporary world). Separately and together, the two heroes contend against the Lords who rule the separate universes, of which the marvelous many-leveled World of Tiers is the center. Mythological and legendary creatures and characters abound: centaurs and harpies, mermaids and Indians, aliens and beautiful women.