Shamshi-Adad I, the first Assyrian king known via his own inscriptions, recorded 38 prior kings and organized them as shown below.
Group & Order
Kings Living in Tents
The first twelve ancestors are the same as Hammurabi of Babylon. Hammurabi had Amorite ancestry, so these twelve ancestors shared between Assyrian and Babylonian must have been nomadic chieftains from before Amorites emerged from the western desert, split apart and settled Mesopotamia in ~2,000 BC. Ilu-Kabkabi, Shamshi-Adad's father, is linked to this line through Apiashal son of Ushpiya. Shamshi-Adad included these undifferentiated ancestors, interjecting his own father a little later, to demonstrate that he was from an old line of ancestral chieftains and thus had legitimately usurped the Assyrian throne.
Kings Who Were Ancestors
Most recent kings are named first, then backward through ancestory.
Kings With Unknown Eponyms
Kings With Names on Bricks
This way people know who built the buildings. Later scribes must have gone around Nineveh and found some sort of old bricks with inscriptions.
Continue to the timeline of Assyria.
Hagens, G. (2005). The Assyrian King List and Chronology: A Critique. Orientalia, 74(1), nova series, 23-41. Retrieved from http://www.jstor.org/stable/43076931