What is the ruling on fasting the first ten days of Muharram, and is there any prophetic hadith concerning that?

The authentic Hadith indicates the permissibility of fasting the ninth and tenth of the month of Muharram. Muslim narrated from Ibn Abbas, may Allah be pleased with both of them, that the Prophet, peace and blessings be upon him, resolved to fast the ninth day if he lived to the next year. Ibn al-Qayyim mentioned that there are three levels for fasting Ashura: the most complete is fasting a day before it and a day after it, followed by fasting the ninth and tenth, and then fasting the tenth alone. The best is to fast the ninth, tenth, and eleventh of Muharram.