The festivals which are prescribed in Islam are Eid al-Fitr and Eid al-Adha, and the weekly Eid of Jumuah. There is no other festival in Islam apart from these three.

Eid al-Fitr takes place after the end of the Month of Ramadan (i.e on the 1st of shawwal which is the 10th month of the Islamic calendar)

Eid al-Adhaa is the tenth day of Dhool-Hijjah, the last (twelfth) month of the Hijri or Islamic calendar. It is, as the Prophet (peace be upon him) said: The greatest day in the sight of Allaah, may He be blessed and exalted, the Day of Sacrifice . . . (Reported by Abu Dawud; see also Saheeh al-Jaami, 1064).