THE ISLAMIC (HIJRI) CALENDAR
The Islamic Calendar, which is based purely on lunar cycles, was first introduced in 638 C.E. by the close companion of the Prophet and the second Caliph, `Umar ibn Al-KHaTTab (592-644 C.E.). He did it in an attempt to rationalize the various, at times conflicting, dating systems used during his time. `Umar consulted with his advisors on the starting date of the new Muslim chronology. It was finally agreed that the most appropriate reference point for the Islamic calendar was the _Hijrah_. The actual starting date for the Calendar was chosen (on the basis of purely lunar years, counting backwards) to be the first day of the first month (1 MuHarram) of the year of the Hijrah. The Islamic (Hijri) calendar (with dates that fall within the Muslim Era) is usually abbreviated A.H. in Western languages from the latinized _Anno Hegirae_. MuHarram 1, 1 A.H. corresponds to July 16, 622 C.E. The Hijrah, which chronicles the migration of the Prophet Muhammad (PBUH) from Makkah to Madinah in September 622 C.E., is the central historical event of early Islam. It led to the foundation of the first Muslim city-state, a turning point in Islamic and world history. To Muslims, the Hijri calendar is not just a sentimental system of time reckoning and dating important religious events (e.g., Siyaam (fasting) and Hajj (pilgrimage to Makkah)). It has a much deeper religious and historical significance.

The Islamic (Hijri) year consists of twelve (purely lunar) months. They are:

(1) MuHarram;
(2) Safar;
(3) Raby` al-awal;
(4) Raby` al-THaany;
(5) Jumaada al-awal;
(6) Jumaada al-THaany;
(7) Rajab;
(8) SHa`baan;
(9) RamaDHaan;
(10) SHawwal;
(11) Thw al-Qi`dah; and
(12) Thw al-Hijjah.

The most important dates in the Islamic (Hijri) year are:
1 MuHarram (Islamic new year);
27 Rajab (Isra & Miraj);
1 RamaDHaan (first day of fasting);
17 RamaDHan (Nuzul Al-Qur'an);
Last 10 days of RamaDHaan which include Laylatu al-Qadar;
1 SHawwal (`iyd al-fiTr);
8-10 Thw al-Hijjah (the Hajj to Makkah); and
10 Thw al-Hijjah (`iyd al-'aDHHaa').

It is considered a divine command to use a (Hijra) calendar with 12 (purely) lunar months without intercalation [Ilyes84], as evident from the following verses of the Holy Qur'an (Trans: A. Yusuf Ali): They ask thee the New Moons Say: They are but signs To mark fixed periods of time In (the affairs of) men And for Pilgrimage. (II:189) The number of months In the sight of Allah Is twelve (in a year) So ordained by Him The day He created The heavens and the earth; Of them four are sacred; That is the straight usage So wrong not yourselves Therein, and fight the Pagans. (IX: 36) Verily the transposing (Of a prohibited month) Is an addition to Unbelief: The Unbelievers are led To wrong thereby: for they make it lawful one year, And forbidden another year, Of months forbidden by Allah And make such forbidden ones Lawful. The evil of their course Seems pleasing to them. But Allah guideth not Those who reject Faith. (IX: 37) Since the Islamic calendar is purely lunar, as opposed to solar or luni-solar, the Muslim (Hijri) year is shorter than the Gregorian year by about 11 days, and months in the Islamic (Hijri) year are not related to seasons, which are fundamentally determined by the solar cycle. This means that important Muslim festivals, which always fall in the same Hijri month, may occur in different seasons.
For example, the Hajj and RamDHaan can take place in the summer as well as the winter. It is only over a 33 year cycle that lunar months take a complete turn and fall during the same season. For religious reasons, the beginning of a Hijri month is marked not by the start of a new moon, but by a physical (i.e., an actual human) sighting of the crescent moon at a given locale. From the Fiqhi standpoint, one may begin the fast in RamDHaan, for example, based on "local" sighting (IKHTILAF AL-MATALE') or based on sighting anywhere in the Muslim World (ITTEHAD AL-MATALE'). Although different, both of these positions are valid Fiqhi positions. Astronomically, some data are definitive and conclusive (i.e. the time of the BIRTH of a new moon).
However, determining the VISIBILITY of the crescent is not as definitive or conclusive; rather it is dependent upon several factors, mostly optical in nature. This makes it difficult to produce (in advance) Islamic calendars that are reliable (in the sense that they are consistent with actual crescent visibility). Efforts for obtaining an astronomical criterion for predicting the time of first lunar visibility go back the the Babylonian era, with significant improvements and work done later by Muslim and other scientists. These efforts have resulted in the development in a number of criteria for predicting first possible sighting of a crescent. However, there remains a measure of uncertainty associated with all criteria developed thus far. Moreover, there has been little work in the area of estimating crescent visibility on global (as opposed to local) scale. Until this happens, no Hijri calendar software can be 100% reliable, and actual crescent sighting remains essential especially for fixing important dates such as the beginning of RamaDHaan and the two `iyds.
The slight differences in printed Islamic calendars, worldwide, can therefore be traced to two primary factors:
(1) the absence of a global criterion for first visibility; and
(2) the use of different visibility criterion (or method of calculation). Weather conditions and differences in the observer's location also explain why there are sometimes differences in the observances of Islamic dates, worldwide.