This series follows a tattooed protagonist through progressive attempts to escape the maze that his race was imprisoned in.
This sounds like The Death Gate Cycle, which is a series with seven books. Wikipedia gives this description of the one race:
Patryns tattooed the runes on themselves and chose their name to mock the Sartan. [...]
The Patryns were captured and imprisoned in the Labyrinth which the Sartan created for their "rehabilitation". The Vortex (or the Sixth Gate) was the entry point to the Labyrinth, where the mensch were temporarily housed during the Sundering itself and where the captured Patryns were eventually placed. The books later reveal that certain members of the Sartan population had objected to The Sundering; these too were consigned to the Vortex and the Labyrinth. In the center of the Labyrinth was the Nexus, a paradise city for the Patryns to live in once they had become "civilized." The Nexus, the Labyrinth, and the Vortex are arranged in concentric circles.