Few doctrines in Islam have engendered as much contention and disagreement as those surrounding the imamate, the office of supreme leader of the Muslim community after the death of the Prophet. In the medieval period while the caliphate still existed, rivalry among the claimants to that most lofty position was particularly intense. The early 5th/11th-century Ismaili dāʿī Ḥamīd al-Dīn al-Kirmānī worked for most of his life in the eastern lands of the Islamic world, principally within the hostile domain of the Abbasid caliphs and the Buyid amirs. At a critical point he was summoned by the daʿwa to Egypt where he taught and wrote for several years before returning once again to Iran and Iraq. About 405/1015, just prior to his move from Iraq to Cairo, he composed a treatise he called Lights to Illuminate the Proof of the Imamate (al-Maṣābīḥ fī ithbāt al-imāmā) in the bold hope of convincing Fakhr al-Mulk, the Shi‘i wazir of the Buyids in Baghdad, to abandon the Abbasids and support the Fatimid caliph al-Ḥākim. For that purpose he produced a long, interconnected series of philosophically sophisticated proofs, all leading logically to the absolute necessity of the imamate. This work is thus unique both in the precision of its doctrine and in the historical circumstance surrounding its composition. The text appears here in a modern critical edition of the Arabic original with a complete translation, introduction and notes.