The Chronicles of Arkham were forms of the Riddler's many challenges.
The Chronicles of Arkham told Batman the story of Amadeus Arkham's family's history from the murder of his wife and daughter, to the capture of Martin "Mad Dog" Hawkins, to Mad Dog's execution, and to Amadeus being admitted into his own Asylum.
In reality, those chronicles were told by Warden Quincy Sharp himself, who believed that he was the Spirit of Arkham. But in reality, he was drugged by Professor Hugo Strange, and went around killing the Arkham Asylum inmates.
Aaron Cash saw Sharp use his own blood and a rusted nail to write his final chronicle, that was addressed directly to Batman on a monitor.
"I am the sprit of Amadeus Arkham. Through my actions, I have saved this cursed city, through my own curse is forever remain in the shadows. My story is carved into the very soul of Arkham and will only be revealed to those dedicated enough to discover it." - Chronicle 1