Few Islamic doctrines have provoked as much division and disagreement as those bound up with the imamate: or the office of supreme leader of the Muslim community following the Prophet's death. In the medieval period, while the caliphate still existed, rivalry among claimants to that position was especially bitter and intense, causing an instability that required resolution. In the early 5th/11th century the great Ismaili thinker Hamid al-Din al-Kirmani was mandated to compose a treatise called Lights to Illuminate the Proof of the Imamate (al-Masabih fi ithbat al-imama) in the bold hope of convincing Fakhr al-Mulk, the Shi'i wazir of the Buyids in Baghdad, to abandon the Abbasids and support instead the Fatimid caliph al-Hakim. For that purpose, he assembled an interconnected series of philosophical proofs, all pointing logically to the absolute necessity of the imamate. This work is unique, both in the precision of its argumentation and in the historical circumstances of its composition. The text appears here in a modern critical edition of the Arabic original with a complete translation, introduction and notes, and will be of immense interest to scholars and students of classical Islam.