The blessed month of Muharram is called the month of Allah! "The best fasting after Ramadan is the month of Muharram". 

Virtue of Fasting in Muharram:
Hadith reports state that the best voluntary fast after Ramadan is fasting in the month of Muharram. This highlights the virtue of fasting during this month, though not necessarily for the entire month.
There is no obligation to fast the whole month, it remains optional for those who wish to do so.

Fasting on Ashura:
The Prophet (ﷺ) emphasized fasting on the day of Ashuraʾ (10th of Muharram) and encouraged adding the 9th or 11th day to it as well. He said that fasting on Ashura expiates the sins of the past year.

A reminder from IOU Founder-Chancellor, Prof. Dr. Bilal Philips, to fast on the 10th of Muharram, adding an extra day before or after. 

May Allah grant us the ability to make the most of it, Ameen.