Kharoṣṭhī script, is an ancient Indic script used by the Gandhara culture of ancient Northwest South Asia (primarily modern-day Afghanistan and Pakistan) to write the Gāndhārī language (a dialect of Prakrit) and the Sanskrit language.
An alphasyllabary, it was in use from the middle of the 3rd century BCE until it died out in its homeland around the 3rd century CE. It was also in use in Kushan, Sogdiana and along the Silk Road where there is some evidence it may have survived until the 7th century in the remote way stations of Khotan and Niya. Kharoṣṭhī. (source)
(a chart of the Kharosthi alphabet, source)
The Kharoṣṭhī script was deciphered by James Prinsep (1799–1840), using the bilingual coins of the Indo-Greeks (Obverse in Greek, reverse in Pāli, using the Kharoṣṭhī script). This in turn led to the reading of the Edicts of Ashoka, some of which, from the northwest of the Indian subcontinent, were written in the Kharoṣṭhī script.
(Paper strip with writing in Kharoṣṭhī. 2-5th century CE, Yingpan, Eastern Tarim Basin, Xinjiang Museum.)
Scholars are not in agreement as to whether the Kharoṣṭhī script evolved gradually, or was the deliberate work of a single inventor. An analysis of the script forms shows a clear dependency on the Aramaic alphabet but with extensive modifications to support the sounds found in Indic languages. One model is that the Aramaic script arrived with the Achaemenid conquest of the region of northwest India in 500 BCE and evolved over the next 200+ years to reach its final form by the 3rd century BCE where it appears in some of the Edicts of Ashoka found in northwestern part of the Indian.However, no intermediate forms have yet been found to confirm this evolutionary model, and rock and coin inscriptions from the 3rd century BCE onward show a unified and standard form.
The study of the Kharoṣṭhī script was recently invigorated by the discovery of the Gandharan Buddhist Texts, a set of birch-bark manuscripts written in Kharoṣṭhī, discovered near the Afghan city of Hadda just west of the Khyber Pass in modern Pakistan. The manuscripts were donated to the British Library in 1994. The entire set of manuscripts are dated to the 1st century CE, making them the oldest Buddhist manuscripts yet discovered.
(SRE Cat. no. 36, From 30-150, Found in Yotkan, The British Museum, source)
The Sino-Kharosthi coins of Khotan are a unique series of coins issued by the kings of Khotan. They brought together the Kushan and Chinese currency systems and created a new coinage which could fit both systems. One side of the coin has a horse and a Kharosthi inscription naming the king of Khotan; the other side depicts a tribal symbol and a Chinese inscription stating the weight of the coin in 'grains' according to the Chinese system. Such coins could be seen as symbols of interaction between cultures where trade played an important role. (source)