Fasting the Day of Ashura' and a Day after or before it.

»Narrated Ibn Abbas: When the Prophet (Peace Be upon Him) came to Medina, he found (the Jews) fasting on the day of Ashura' (i.e. the 10th day of the month of Muharram). They used to say: "This is a great day on which Allah saved Moses and drowned the folk of Pharaoh. Moses observed the fast on this day, as a sign of gratitude to Allah." The Prophet said, "I am closer to Moses than them." So, he observed the fast (on that day) and ordered the Muslims to fast on it. «([1])

»Abu Qatadah narrated that: the Prophet (PBUH) said: "Fast the Day of Ashura', for indeed I anticipate that Allah will forgive (the sins of) the year before it." «([2])

»Abdullah ibn Abbas reported that the Messenger of Allah (Peace Be upon Him) said: If I live till the next (year), I would definitely observe fast on the 9th, and the narration transmitted by Abu Bakr is: "He meant the day of Ashura'." «([3])

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([1]) Sahih al-Bukhari – Kitab Ahadith al-Anbya' (7933).

([2]) Sunan ibn Majah – Kitab al-Sayam (8371), Sunan Abi Dawoud – Kitab al-Sawm (5242), Sunan al-Tirmidhi – Kitab al-Sawm (257).

([3]) Sahih Muslim – Kitab al-Sayam (4311).