Light Yagami found a notebook after it fell from the sky. Light discovers that the notebook has the power to kill anyone he wants, so he uses the Death Note to kill criminals (from minor to high-level crimes).

Light's first victim was a man who kidnapped children and a teacher, followed by a harasser and rapist.

Light Yagami knows that killing is wrong, but he's only doing it because he wants a world of justice. (That's what he wanted at first; later it was pure ego...)

After the Justice of the God Kira appeared, the crime rate dropped dramatically.