The Kharosthi alphabet was invented sometime during the 3rd century BC and was possibly derived from the Aramaic alphabet. It was widely used in northwest India and central Asia until the 4th century AD.
Unlike the Brahmi script, which was invented at around the same time and spawned many of the modern scripts of India and South East Asia, Kharosthi had no descendants.
Kharoshti was deciphered by James Prinsep and others around the middle of the 19th century. Since then further material has been found and the script is now better understood.
Gandhari and Sanskrit
Kharosthi information (includes free Kharosthi font)
Kharosthi Unicode proposal submitted by Andrew Glass, Stefan Baums, and Richard Salomon - the above
script chart and text sample is based on this
A Preliminary Study of Kharosthi Manuscript Paleography, by Andrew Glass
ALPHABETUM - a Unicode font specifically designed for ancient scripts, including classical & medieval Latin, ancient Greek, Etruscan, Oscan, Umbrian, Faliscan, Messapic, Picene, Iberian, Celtiberian, Gothic, Runic, Old & Middle English, Hebrew, Sanskrit, Old Nordic, Ogham, Kharosthi, Glagolitic, Old Cyrillic, Phoenician, Avestan, Ugaritic, Linear B, Anatolian scripts, Coptic, Cypriot, Brahmi, Old Persian cuneiform: http://guindo.pntic.mec.es/~jmag0042/alphabet.html
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