Leeming, an emeritus professor of English at the University of Connecticut, is best noted for his biography of James Baldwin. He has also produced a stream of books on world mythology.
As usual, the ancient Near East carries a heavy burden since "the events and stories under consideration here cannot be reasonably separated from the recent history." The mythological past is the political present, especially for "nationalized religious traditions, particularly Israeli Jew and Arab Muslim (with significant Western Christian participation)." But Leeming's goal is ecumenical to say the least; "with nonexclusionary vision, other people's religious narratives can be seen as tribe-defining cultural dreams and as significant metaphors that can speak truthfully to people across cultural and sectarian boundaries." In his view only "fundamentalists" feel otherwise.
The volume provides highly schematic and often poorly informed background chapters on prehistory, the Bronze Age, Iron Age, and "Jews, Christians and Muslims." These are followed by individual chapters on the mythology of prehistory, Mesopotamia, Egypt, Anatolia, the western Semites, and Arabia and the Muslims. Some of the primary gods and mythological cycles are introduced, particularly heroes and creation myths. These hardly exhaust, or begin to describe, the vast range of mythological motifs, their interaction and significance, across some ten thousand years.
The volume is produced entirely from secondary sources without command of the many languages in question. This is not an impossible obstacle, of course, provided there is sensitivity to the material and its complexities. A prerequisite is consulting editio princeps of the many texts cited, or collections such as the classic Ancient Near Eastern Texts Related to the Old Testament and its modern descendents. Sadly, Leeming relies to an unreasonable degree on general articles in the Eliade-edited Encyclopedia of Religion, and non-experts such as Joseph Campbell and Karen Armstrong, rather than far more authoritative monographic syntheses.
There have been numerous books dealing with Near Eastern mythology from the standpoint of individual cultures and in comparative terms by estimable scholars past such as Sabatino Moscati and Samuel Noah Kramer, and more recently Stephanie Dalley and Gwendolyn Leick, to name but a few. They are still to be recommended.
 James Baldwin: A Biography (New York: Henry Holt & Company, 1995).