The first Muslim month is Muharram and Muharram is observed on the tenth day of this month.
It is celebrated with great fervour by the Muslims especially the Shia community.
This festival starts at the 1st day of Muharram and lasts for 10 days until 10th of Muharram. Muharram is the first month of Islamic calendar.
Web : http://www.festivalsofindia.in/Muharram/