Before his work titled Arithmetica became a source of inspiration for the emerging field of Number Theory from the 17th century onwards, Diophantus was known mainly as an algebraist. This volume — which offers the translation into modern Greek of the ten surviving books of the work, along with thorough conceptual, historical, and mathematical commentary — demonstrates that the method by which Diophantus solved arithmetic problems shows full conceptual and methodological affinity with the pre-modern algebra practiced many centuries later in Arabic, Latin, and European vernacular languages, on the one hand, and that this algebra differs fundamentally from the modern algebra introduced by François Viète and René Descartes, on the other. It also examines other surviving traces of ancient Greek algebra and traces the influence of Arithmetica on medieval Islam, Byzantium, and the European Renaissance, up until the work's publication by Bachet de Méziriac in 1621.