What are the authoritative sources a judge must use for judgment?

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A judge must rule according to the Book of Allah (the Quran). If the ruling is not found therein, the judge must rule according to the Sunnah of the Messenger of Allah, peace be upon him. If neither source provides a ruling, the judge must then exercise his independent legal reasoning (Ijtihad). This methodology was affirmed by the Prophet, peace be upon him, when approving Mu'adh's stated method of judgment.