The Zij-i Ilkhani (Persian: زیج ایلخانی, “Ilkhanid Tables”) is a major astronomical handbook and star catalogue compiled in the thirteenth century at the Maragheh Observatory in northwestern Persia under the direction of Nasir al-Din al-Tusi. Commissioned by the Ilkhanid ruler Hulagu Khan and completed around 1272, it represents one of the most comprehensive works of Islamic mathematical astronomy and served as a standard reference for observational and computational astronomy across the Islamic world, parts of Europe, and East Asia for several centuries.

The Zij-i Ilkhani was produced at the Maragheh Observatory, founded circa 1259 under Hulagu Khan's patronage following the Mongol conquest of Persia. Al-Tusi assembled a team of astronomers drawn from across the Islamic world and possibly including Chinese scholars, making the project unusually international for its era. The work is organized in the traditional zij format - a genre of Islamic astronomical handbook pairing planetary tables with the mathematical and observational procedures needed to use them.

The text includes tables of planetary motion based on a combination of new observations made at Maragheh and a critical reanalysis of earlier Ptolemaic and Islamic sources. It also contains star catalogues, trigonometric tables, calendrical conversion tables covering multiple calendar systems (including the Hijri, Persian, Syriac, and Chinese calendars), and sections on spherical astronomy and mathematical geography. The planetary models developed in connection with the Zij-i Ilkhani are notable for incorporating modifications to Ptolemaic epicyclic theory, including the device later known as the Tusi couple, which addressed mathematical inconsistencies in Ptolemy's Almagest.

The Zij-i Ilkhani was widely copied and translated. It circulated in Persian and was rendered into Arabic and, eventually, into Latin. Its star catalogue and planetary tables influenced subsequent zijes compiled in the Islamic world, including works produced in the Timurid and Ottoman periods. It is among the Islamic astronomical texts sometimes cited in discussions of continuity between medieval Islamic astronomy and early modern European astronomy, including the work of Copernicus, though the precise pathways of transmission remain a subject of scholarly inquiry.

There is broad consensus among historians of science that the Zij-i Ilkhani is a significant work in the history of astronomy and that the Maragheh school produced innovations in planetary theory. The extent to which these innovations directly influenced Renaissance European astronomy is a more contested question; see Zij-i Ilkhani - History of Science Consensus.

• Maragheh-Copernicus transmission - Some historians of science argue that specific mathematical devices found in the Zij-i Ilkhani and related Maragheh texts appear in Copernicus's De Revolutionibus, suggesting direct or indirect borrowing. Others contend the parallels reflect independent development from shared Ptolemaic foundations. See Copernicus Transmission Viewpoint.

• Scope of innovation - Assessments differ on whether the Maragheh modifications represent a fundamental break from Ptolemaic astronomy or a sophisticated reform within its framework. See Scope of Innovation Viewpoint.

• Zij-i Ilkhani - History
• Maragheh Observatory
• Nasir al-Din al-Tusi
• Islamic Astronomy
• Zij
• Ptolemaic Astronomy
• Zij-i Ilkhani - History of Science Consensus

1. E. S. Kennedy, “A Survey of Islamic Astronomical Tables,” Transactions of the American Philosophical Society, New Series, 46:2 (1956), pp. 123-177.
2. George Saliba, A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam (New York: New York University Press, 1994).
3. F. Jamil Ragep, Nasir al-Din al-Tusi's Memoir on Astronomy (al-Tadhkira fi 'ilm al-hay'a), 2 vols. (New York: Springer, 1993).
4. Aydin Sayili, The Observatory in Islam (Ankara: Turkish Historical Society, 1960), pp. 187-223.
5. Noel Swerdlow and Otto Neugebauer, Mathematical Astronomy in Copernicus's De Revolutionibus (New York: Springer, 1984), Part One, ch. 2.