ISLAMIC CALENDAR or HIJRI CALENDAR
The Islamic or Hijri calendar is a lunar calendar. It contains 12 months that are based on the motion of the moon. Islamic calendar is consistently shorter than a solar year by about 10 days every year, and therefore it shifts with respect to the Gregorian calendar. 
In pre-Islamic Arabia, it was customary to identify a year after a major event which took place in it. Thus, according to Islamic tradition, Abraha, governor of Yemen, then a province of the Christian Kingdom of Aksum (Ethiopia), attempted to destroy the Kaaba with an army which included several elephants. The raid was unsuccessful, but that year became known as the Year of the Elephant, during which Prophet Muhammad (May Allah honour Him and grant Him peace) was born. Most equate this to the year 570 CE, but a minority use 571 CE.
The first ten years of the Hijra were not numbered, but were named after events in the life of Muhammad according to Abu Rayhan al-Biruni (May Allah have Mercy on Him).
In 638 CE (17 AH), Abu Musa Ashaari(R), one of the officials of the Caliph Umar(R) in Basrah, complained about the absence of any years on the correspondence he received from Umar(R), making it difficult for him to determine which instructions were most recent. This report convinced Umar(R) of the need to introduce an era for Muslims. After debating the issue with his counsellors, he decided that the first year should include the date of Muhammad's (May Allah honour Him and grant Him peace) arrival at Madina (known as Yathrib, before Muhammad's arrival). Uthman ibn Affa(R) then suggested that the months begin with Muharram, in line with the established custom of the Arabs at that time. The years of the Islamic calendar thus began with the month of Muharram in the year of Muhammad's (May Allah honour Him and grant Him peace) arrival at the city of Madina, even though the actual emigration took place in Safar and Rabi' ul Awwal. Because of the Hijra, the calendar was named the Hijra/Hijrah calendar. The Arabic word Hijrah means emigration. 
There are twelve months in Islamic Calendar as mentioned in Qur’an: Surely the number of months with Allah is twelve months in Allah's ordinance since the day when He created the heavens and the earth, of these four being sacred…” Qur’an.Surah Tawbah 9:36.
The Twelve months of Islamic Calendar are as follows:
9. Ramadhan or Ramzan
12. Zul-Hijjah 
Abu Bakrah (R), reported that the Prophet Muhammad (May Allah honour Him and grant Him peace) said: "The year is twelve months of which four are sacred, the three consecutive months of Dhu'l-Qa'dah, Dhu'l-Hijjah and Muharram, and Rajab which comes between Jumada and Sha'ban." Sahih Al-Bukhari 3197(NE) [Vol 4:419 ], 4708 and 5550, Sahih Muslim 1679 and Abu Dawud 1947