Abū Muḥammad ʿAbd Allāh ibn Yūsuf ibn al-Ḥāfiẓ (Arabic: أبو محمد عبد الله بن يوسف بن الحافظ‎; 1151–1171), better known by his regnal name al-ʿĀḍid li-Dīn Allāh (Arabic: العاضد لدين الله, lit. 'Strengthener of God's Faith'), was the fourteenth and last caliph of the Fatimid dynasty, and the twenty-fourth imam of the Hafizi Isma'ili branch of Shi'a Islam, reigning from 1160 to 1171.

Like his two immediate predecessors, al-Adid came to the throne as a child, and spent his reign as a puppet of various strongmen who occupied the vizierate. He was a mostly helpless bystander to the slow collapse of the Fatimid Caliphate. Tala'i ibn Ruzzik, the vizier who had raised al-Adid to the throne, fell victim to a palace plot in 1161, and was replaced by his son, Ruzzik ibn Tala'i. Ruzzik was in turn overthrown by Shawar in 1163, but the latter lasted only a few months in office before being overthrown by Dirgham. The constant power struggles in Cairo enfeebled the Fatimid state, allowing both the Crusader Kingdom of Jerusalem and the Sunni ruler of Syria, Nur al-Din, to advance their own designs on the country. The Crusaders repeatedly invaded Egypt, extracting tribute and ultimately aiming to conquer it; in turn, Nur al-Din supported Shawar's bid to retake the vizierate from Dirgham, and sent his general Shirkuh to counter the Crusaders. For a while, Shawar played the Crusaders and Syrians against one another, but in January 1169, Shirkuh overthrew Shawar, occupied Cairo and became vizier. When Shirkuh died shortly after, he was succeeded by his nephew, Saladin.

Saladin was initially conciliatory towards al-Adid, but quickly consolidated his hold over Egypt, and proceeded to gradually dismantle the Fatimid regime. Fatimid loyalists in the army were purged and replaced with Syrian troops, culminating in the failed mutiny of the Battle of the Blacks. Members of Saladin's family were installed as governors, the civilian bureaucracy was largely won over to the new regime, and al-Adid was sidelined even from ceremonial roles. Finally, Isma'ilism was progressively abolished as the state religion in favour of Sunni Islam, culminating in the official proclamation of Abbasid suzerainty in September 1171. Al-Adid died a few days later. His family was placed under house arrest, and Isma'ilism persecuted by Saladin's new Ayyubid regime, so that within a century after the fall of the Fatimid regime it had almost disappeared in Egypt.

The future al-Adid was born on 9 May 1151, according to the commonly accepted date, provided by the thirteenth-century historian Ibn Khallikan. Other authors, however, give earlier years, in 1145 or 1149. He was the son of the Fatimid prince Yusuf, a younger son of the eleventh Fatimid caliph, al-Hafiz li-Din Allah (r. 1132–1149). Yusuf was one of the oldest surviving sons of al-Hafiz, but at the latter's death, the powerful vizier Salim ibn Masal installed al-Hafiz's youngest son, the 16-year-old Isma'il, as caliph with the regnal name al-Zafir bi-Amr Allah. Al-Zafir was assassinated in 1154 by his vizier, Abbas ibn Abi'l-Futuh. The vizier raised al-Zafir's five-year-old son Isa to the throne under the name al-Fa'iz bi-Nasr Allah, and had Yusuf and another older brother of al-Zafir's, Jibril, executed on the same day.

By this time, the Fatimid dynasty was in decline. The official doctrine of Isma'ili Shi'ism had lost its appeal and was weakened by succession disputes and schisms, and the dynasty's legitimacy was increasingly challenged by a Sunni resurgence in Egypt. As the fate of al-Zafir shows, the Fatimid caliphs themselves had become virtual puppets in the hands of their powerful chief ministers: the viziers bore the royal title of sultan, and their names were included in the Friday sermons and on coins alongside the caliph's. The historian Yaacov Lev sums up the state of Egypt as "The Sick Man on the Nile". The weakness of the Isma'ili Fatimid regime was noticed by its Sunni rivals, the Abbasids of Baghdad: in 1154, the Abbasid caliph al-Muqtafi (r. 1136–1160) issued a diploma appointing the Zengid ruler of Syria, Nur al-Din (r. 1146–1174), as the nominal ruler of Egypt.

Al-Fa'iz was of sickly disposition and died on 22 July 1160, aged only eleven years. Lacking a direct heir, nine-year-old al-Adid was elevated to the throne by another all-powerful vizier, Tala'i ibn Ruzzik, on 23 July 1160. To further cement his hold over the caliph, Ibn Ruzzik married him to one of his daughters. Throughout his reign, al-Adid was little more than a figurehead monarch, effectively a puppet in the hands of courtiers and strongmen who disputed with one another over the spoils of the tottering Fatimid state. As the French orientalist Gaston Wiet comments, "The Arab writers seem uncertain, and intermittently attribute to him stray impulses of revolt, which had little success [...] in general the caliph looked on helplessly at a shattering series of tragic incidents of which he himself was finally to be the victim."

As a result of the lack of information about al-Adid, his personal traits are not well known. Ibn Khallikan reports that he was violently pro-Shi'a, while the only physical description of him is by the Crusader historian William of Tyre, on the occasion of an audience with Crusader leaders: his face was veiled, but his appearance was described as that of "a young man of an extremely generous disposition, whose first beard was just appearing; he was tall, of swarthy complexion and good frame."

Ibn Ruzzik, who was inclined towards the Twelver branch of Shi'ism, was assassinated on 11 September 1161, possibly with the knowledge of the young caliph, as the deed was said to have been instigated by one of al-Adid's aunts, Sitt al-Qusur. Nevertheless, his place was immediately taken by his son, Ruzzik ibn Tala'i, who likewise denied any power to the caliph. The new vizier had Sitt al-Qusur strangled, while al-Adid came under the auspices of another aunt, who had to swear that she had not been involved in the murder plot. Soon after, the new vizier suppressed the last revolt by a claimant of the rival Nizari line of the Fatimid dynasty, Muhammad ibn al-Husayn ibn Nizar: arriving from the Maghreb (western North Africa), he had tried to raise Cyrenaica and Alexandria in revolt, but was captured and executed in August 1162.