William T. Vollman, whose writing veers between lyric originality and hyperinflation, has embarked upon a fictional history of the American continent from the time of the Vikings to the present day.

"The Ice Shirt" is the first of a projected seven-part cycle that Vollman is calling "Seven Dreams." Dream One deals with Norse gods and early kings along with the wanderings of Viking sailors, the settlements in Iceland and Greenland and the brief, early landings in Vinland, somewhere on our North Atlantic coast.

The narrative focus is upon the Norse venturers, particularly Erik the Red, who went from Iceland to colonize Greenland; and upon Erik's children--Leif Eriksson, Freydis Eriksdottir, Thorstein Eriksson and his wife, Gudrid--who went from Greenland to Vinland. The thematic focus is on the encounter between these venturers and those who were already there: the Inuit or Eskimos of Greenland, and the Mic Mac Indians on the mainland.

The theme that emerges is that of man-out-of-nature versus man-in-nature, the despoiler and the despoiled, Cain versus Abel, Eden after and before the apple. Vollman's Vikings are the human spirit bent on power over Earth and heaven; his Inuits and Mic Macs are the human spirit as fellow denizen of heaven and Earth along with gods and snail darters. The original landfall seems to be original sin.

Vollman writes in a dizzying assortment of narratives. For his Norsemen, he uses the Icelandic Sagas, supplemented by the mythological tales in the Eddas. For his Inuits and Mic Macs, he uses collections of Native American tales and studies of their folkways.

To these he adds all manner of things. A tale of a male Inuit precursor changing into a woman comes side by side with a conversation with a San Francisco transvestite. In an account of the Greenlanders on Baffin Island, he writes the story of a friend who visited the place in 1984 and whom he calls, saga-style, Seth Pilsk the Thin. (He refers to himself as William the Blind.) And he seeds his story with brief accounts of his own travels in present-day Greenland.

His styles vary equally. For the first part of the book, relating the struggles of Norse kings and gods, and the black, bloody magic of early legends--warriors transformed into bears and wolves, forest queens who incinerate their suitors--he writes with a choked and hard-to-follow grandiloquence. Later, in his account of Freydis, Erik the Red's daughter, visiting the underworld, Vollman's writing is so Baroque and bombastic as to approach campiness.