The history of the passage of the extraordinarily brilliant and fundamental mathematical discoveries of the ancient Indian mathematician, Brahmagupta (598-665 c.e.) from India to Arabia and then to Europe, through the centuries, has been vividly described. This article endeavors to appreciate Brahmagupta's position as an original creative mathematician in the perspective of world mathematics. This paper primarily concentrates on the history of the Brahmagupta's mathematics and his transmission to the Arab countries. The methodology adopted has a composite structure: history and mathematics. We have discussed Brahmagupta's original contributions, which are contained in two illustrious treatises-the Brahma-sphutasiddh anta and the Khan. d.a-khadyaka-composed in Sanskrit verses. Brahmagupta's original method of solving an indeterminate quadratic equation in two variables has been presented in some detail. The details of the Indian and Arab scholars and others involved in the intellectual scientific-mathematical transmission of knowledge processes, the roles played by the then rulers of Indian and the Arab countries in this type of transmission operation, the socio-political situations in these countries are presented. It has been concluded that Brahmagupta's mathematics is now a part of the stat shared heritage of humankind. © 2011 Springer Science+Business Media, LLC.