The book is available at the Sacred Texts Archive, and the links below are to that edition online.
Chapter I. The Scope and Significance of Sumerian Mythology
Chapter II. Myths of Origins
—The Creation of the Universe
—The Organization of the Universe
—Enlil and Ninll: the Begetting of Nanna
—The Journey of Nanna to Nippur
—Emesh and Enten: Enlil Chooses the Farmergod
—The Creation of the Pickax
—Cattle and Grain
—Enki and Ninhursag: the Affairs of the Watergod
—Enki and Sumer: the Organization of the Earth and Its Cultural Processes
—Enki and Eridu: the Journey of the Water-god to Nippur
—Inanna and Enki: the Transfer of the Arts of Civilization from Eridu to Erech
—The Creation of Man
Chapter III. Myths of Kur
—The Destruction of Kur: the Slaying of the Dragon
—Inanna's Descent to the Nether World
Chapter IV. Miscellaneous Myths
—The Deluge
—The Marriage of Martu
—Inanna Prefers the Farmer
Chapter V. References and Notes