As the Muslims have their own Muslim festivals and rituals that are entirely different from other non Muslim religions that is why Muslims have their own calendar called as Islamic calendar
Who introduce Islamic calendar
Islamic calendar was introduced in 638 CE (16 AH) by the second caliph Umar ibn Al-Khattab in order to get rid of different calendar and their dating system that were used at that time.
The caliph after discussing with their companions decided that from hijrah the Muslim calendar will start it was the time when Holy Prophet migrated from Makah to Medina. It was a turning point in the history of Muslims and thus became the start of an Islamic calendar.
The calendar and its month
Islamic calendar is completely a lunar calendar comprises of twelve months based on movement of moon. The Islamic calendar is comparatively shorter than the Christian calendar. The appearance of new moon decides the start of new month. The names of the months of Islamic calendar are (1) Muharram, (2) Safar, (3) Rabi` Awwal, (4) Rabi` Thani, (5) Jumada Awwal, (6) Jumada Thani, (7) Rajab, (8) Sha`ban, (9) Ramadan, (10) Shawwal, (11) Dhul- Qi`dah, (12) Dhul- Hijjah.
The dates that hold great importance in Islamic religion are 1 Muharram (Islamic New Year); 10 Muharram (Day of `Ashura’); 27 Rajab (Israa’ and Mi`raj); 1 Ramadan (first day of the month of fasting); the last ten days of Ramadan, which include (Laylat Al-Qadr); 1 Shawwal (`Eid Al-Fitr); 8 - 10 Dhul-Hijjah (Hajj); 9 Dhul-Hijjah (Day of `Arafah); 10 Dhul-Hijjah (`Eid Al-Adha).