The Hijri or Islamic calendar is based on a lunar month of 29 to 30 days, with the day starting at sunset.
They ask you, (O Muhammad), of new moons. Say: They are fixed seasons for mankind and for the pilgrimage… (Quran 2:189)
The new moon announces the arrival of a new month, but due to differences in the weather (rain and fog, etc.) that may prevent a clear view of the moon, or due to great distances between countries, the start of a new month is neither definite nor conclusive.
Therefore scientists have developed a number of norms to help predict when the first sighting of the crescent moon will be, but there will be small discrepancies between countries when determining the birth of the crescent heralding the month of Ramadan and the first day of the following month, indicating the end of the fast.
The Islamic year consists of twelve months:
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 most important dates in the Islamic calendar 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).
However, the dates of so many of these events, such as that of Laylat Al-Qadr and the Prophet Muhammad’s journey of Israa’ and Mi`raj, have not been conclusively specified, and there has been some uncertainty about their exact dates.
Four of the twelve months are sacred: Rajab, Muharram, Dhul-Qi`dah, Dhul- Hijjah).
In the pre-Islamic period, raids among the Arab tribes were forbidden and hunting was halted during these months. Islam inherited and approved this practice.
Fighting (killing) is prohibited during these sacred months except in self-defense.
Since the Islamic calendar is lunar, its year is 10 or 11 days shorter than the Gregorian year. This means that Muslim months fall in different seasons.
For example, Ramadan and Hajj can fall in the summer as well as in the winter. It takes about 33 years for the Islamic dates to rotate through the solar seasons.
The dating of the Islamic calendar was introduced by the second caliph, `Umar ibn Al-Khattab, in 638 CE (16 AH) in an attempt to circumvent all the various conflicting dating systems used during his time.
After consulting his companions, he set the Hijrah—the immigration of the Prophet (peace and blessings be upon him) from Makkah to Madinah—as the most appropriate reference to the new Islamic era.
The Hijrah, historically speaking, is the central event of early Islam, the turning point in Islamic history that led to the foundation of the first Muslim state.
Compiled by Reading Islam Team.
SOURCE: https://aboutislam.net/reading-islam/understanding-islam/who-was-the-first-to-invent-the-islamic-calendar/
