The Old Babylonian period (ca. 1894–1595 BCE) occurs after the demise of the Neo-Sumerian Dynasty in Mesopotamia. Situated on the Euphrates River, the city of Babylon rose to its greatest prominence in the eighteenth century BCE, when the Amorite king Hammurabi (r. 1792–1750 BCE) united a state stretching from the Persian Gulf to Syria. Babylon was ruled by Hammurabi’s successors until 1595 BCE, when a Hittite incursion into Mesopotamia reached Babylon, bringing an end to the kingdom. One well-known work of art from the Old Babylonian period is the Stele of Hammurabi (British Museum, London). Web resources here and here.
The Burney Relief (a.k.a. “The Queen of the Night”). Probably from Tello (ancient Girsu), Iraq. Painted terracotta. Ca. 1750 BCE. British Museum, London.