While Batman and the supporting characters share a similar background to those in the main continuity, parts of the characters origin and stories on Earth-31 have been slurred or altered. According to Miller, the Batman that appears in All-Star Batman and Robin, the Boy Wonder is the same character who appears in Batman: Year One, The Dark Knight Returns, and The Dark Knight Strikes Again. Unlike Batman on Earth-0 (the mainstream continuity), this Batman is much darker and significantly more brutal than his counterpart. He takes joy in causing his victims heavy amounts of pain, going as far as severely pummeling and burning his victims for his amusement. The only story that crosses into Earth-0 is Batman: Year One.
Batman: Year One
For more information: Batman: Year One
The first appearance of Batman in this universe, is also the widely accepted version of how he fist appeared in the main continuity. The story begins as Bruce Wayne returns to Gotham City after being away for around a decade, traveling the world being taught in martial arts, physical conditioning, and science. Lieutenant James Gordon is a police officer new to Gotham, just transferring form the Chicago Police Department. He and his wife Barbara are trying to settling into the new city when they both realize that Gotham has a very gritty underbelly, containing lots of crime and corruption. Soon after moving into Gotham, Gordon witnesses his new partner Detective Flass, whom he's never had a good feeling towards, bullying a young teen. Flass was always resentful and disrespectful towards Gordon, immediately sensing his prideful and high moral upon meeting him. Detective Flass becomes a main antagonist in the book opposing Gordon. The two clash on a number of occasions throughout the story on multiple levels, going as far as physically fighting one another.
By the end, Gordon is seen as a "celebrity cop" and Batman has managed to strike fear into the heart of Gotham's corrupt police force, and the criminals occupying the city. After a series of events that find Jim Gordon in a fist fight with Jimmy Vitti (Carmine Falcone's nephew) on a bridge, Bruce Wayne who had also been after Vitti ends up saving Gordon's infant child after Vitti who had kidnapped him and the child both fall off of the bridge. Gordon who previously dropped and broken his glasses, realizes he's standing in front of an unmasked Batman, but lets Bruce go, stating "I'm practically blind without my glasses. In the final scene, it shows Gordon awaiting Batman on top of a building, were he plans to tell him about someone named "Joker" who plans to poison the reservoir.
The Dark Knight Returns
For more information: The Dark Knight Returns
At this point in the universe, it has been ten years since anyone has seen or heard from the Batman. Bruce Wayne has given up the cape and cowl for life of drinking and adrenaline rushes; Dick Grayson and Bruce have not spoken for years; Jason Todd is dead. America is embroiled in a heating-up Cold War with the Soviet Union. Ronald Reagan is the President of the United States, and he is confidantes with Superman. Gotham City has further degraded into a cesspool of crime and poverty, while the media sensationalizes tragedy for entertainment value. Commissioner Gordon is being forced to retire while a new youth street gang called the Mutants seemingly rules the streets. With all these factors coming together and the return of some old foes, the Batman reemerges with the assistance of a new Robin (Carrie Kelly) to restore his vision of justice to this world.