The frame
The chronology list of the Met's timeline for Iraq (Mesopotamia), 500-1000 A.D., names "Rule of the Rightly Guided Caliphs, ca. 636/37-61", "Umayyad rule, 661-750" and "Abbasid caliphate, 750-1258". According to the overview, in the seventh century this area was conquered by Arab armies and transformed into the center of Islamic civilization; under the Abbasid caliphate the focal point of Islamic political and cultural life shifted eastward from Syria to Iraq, and in 762 Baghdad, the circular "City of Peace", was founded as the new capital. This page brings these stages together, from the conquest to 1258. Source 1.
Boundaries and overlaps
The start is not a single date: the chronology list gives "ca. 636/37", while the key-events entry for 634-644 says that Arab armies under the banner of Islam conquered Mesopotamia. Within the Abbasid period, the chronology list for 1000-1400 adds that the caliphate was "controlled by Buyid dynasty, 945-1055 and Seljuq sultanate, 1055-1194". Here too the source is not uniform: on the page for 500-1000, the entry for 945 gives the Buyid dynasty the years 932-1062. In the north the Jazira stands apart: according to the timeline, under the Zengid Atabegs of Mosul, 1127-1262, northern Mesopotamia became a great economic, political and artistic center, and their rule crosses this page's boundary of 1258. Sources 1, 2.
On this site
Two articles are placed in this period. "Samarra: a short-lived Abbasid capital" reads UNESCO's page on the city, a capital from 836 to 892, whose site is 41.5 km long. "The Mustansiriyya Madrasa: an Abbasid college in Baghdad" reads the Met's timeline on the madrasa of 1228-33, from the brief Abbasid revival before 1258. Sources 3, 2.