The Muslim lunar calendar, consisting of twelve lunar months. Because it is purely lunar, it is eleven days shorter than the Gregorian calendar and thus festival and feast dates such as Ramadan precess through the seasons, which are solar-based.

The Hijra's zero-point is the first day of the first lunar month of the year of Mohammed's flight from Mecca to Medina and the establishment of the first Musilm city-state. MuHarram 1, 1 A.H. (Anno Hagira) corresponds to July 16, 622 A.D.

What is interesting about the hijra is that is that the start of months (including the all-important month of Ramadan) is based not on the theoretical precise moment of a new moon but on an actually observed thin crescent. If you (or anyone with whom you're in contact) haven't seen the new moon, the month hasn't started yet. Because of this, it is impossible to predict precisely when a holy day will take place, even though the technical moment of the new moon can be determined with great precission.

As a side note in a similar vein, the beginning and end of any given day within the Muslim calendar is said to be the moment at which one can distinguish between a white thread and a black thread held up to the sky.