The Aramaic language was the international trade language of the ancient Middle East. Originated in what is modern-day Syria, between 1000 and 600 BCE it became extremely widespread, spoken from the Mediterranean coast to the borders of India. Its script, derived from Phoenician and first attested during the 9th century BCE, also became extremely popular and was adopted by many people, both with or without any previous writing system.
The following is the Aramaic script:
One interesting innovation in Aramaic is the _matres lectionis_ system to indicate certain vowels. Early Phoenician-derived scripts did not have letters for vowels, and so most texts recorded just consonants. Most likely as a consequence of phonetic changes in North Semitic languages, the Aramaeans reused certain letters in the alphabet to represent long vowels. The letter 'aleph was employed to write /ā/, he for /ō/, yodh for /ī/, and waw for /ū/.
Aramaic flowered into myriads of different variants, which eventually became the script of many nations in the Middle East. One important example is the square Hebrew script. Writing, derived from Phoenician, began to appear in Palestine around the 10th century BCE, and the Old Hebrew script was one of them. However, bythe 6th century BCE, an Aramaic-derived script, appropriately called the Jewish script, began to replace the Old Hebrew script. It isthe Jewish script that eventually evolved into the modern square Hebrew script.
Another important Aramaic offshoot is the Nabataean script, which eventually evolved into the Arabic script, replacing older scripts of Arabia such as South Arabian and Thamudic. The Aramaic script was also the source of Middle Eastern scripts such as Syriac, Mandaic, Palmyrene, and Hatran.
Further afield, Aramaic is also thought to have influenced script development in India. Many of the signs in the Kharosthi and Brahmi scripts bear some resemblance to similar-sounding letters in Aramaic. It is unclear what is the exact relationship between Indic scripts and Aramaic, but Aramaic was definitely trasmitted to northwestern India and might have influenced to some extent the evolution of writing in South Asia.
Finally, another important branch of Aramaic would be the Pahlavi script, which in turn led to the Avestan and Sogdian scripts. Through Sogdian, writing in Central Asia blossomed, spawning Uighur, Mongolian, and Manchurian, which would be the eastern-most descent of Aramaic.
As you can see, Aramaic was a kind of "nexus" in the history of writing in Asia. It gave birth to writing systems used by vastly different nations in drastically different geographical locations.