Arabic is in the Semitic language group, which seems to have originated somewhere near modern Syria, and to have spread from there through Lebanon, Israel, and Jordan down to the Arabian peninsula.
Until the time of Mohammed, in the 600s AD, Arabic was mainly spoken and not written. Still, there are some written records from the Arabian peninsula from before the 600s AD. These are called Sabataean. But they are only short inscriptions in stone, not really literature.
After the Islamic conquests of the late 600s AD, people soon began to speak Arabic all over the Islamic Empire, from Afghanistan to Spain, and people speak Arabic in even more places today (though not in Spain). By 1000 AD, people spoke Arabic in India.
Many people began to write in Arabic. Among the first things to be written was the Koran, but soon many scientific texts and medical books and math books were written in Arabic, and also stories like the Arabian Nights or the story of Aladdin. There were many Arab historians, geographers, philosophers, and poets. Also, in the eastern part of the Islamic Empire, many people spoke and wrote in Persian (an Indo-European language). One famous Persian story, written about 1000 AD, is the story of Sohrab and Rustem.
Here's a song by Yusuf Islam (who used to be Cat Stevens) to teach the Arabic alphabet:
As Turkic and Altaic people from Central Asia moved into West Asia, beginning in the later medieval period, many people also told or wrote stories in Turkish. You can compare stories about the trickster Nasruddin to African Anansi stories.
To find out more about Arabic and Islamic literature, check out these books from Amazon or from your local library: