The Chronicles of Arkham were forms of the Riddler's many challenges.
The Chronicles of Arkham told the story of Amadeus Arkham telling Batman about his family's history to the murder of his wife and daughter, to the capture of Martin "Mad Dog" Hawkins, to Mad Dog's execution, 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.