The Computer Establishment, by Katharine Davis Fishman. New York: Harper & Row. 468 pp. $20.95

This is the story of Big Brother and the Seven Dwarfs, as they were once known in computerland. (As author Katharine Fishman noted in a recent radio interview, computer people don't seem to mind mixing their metaphors.)

Big Brother is, of course, the gargantuan IBM, referred to by its own executives simply as ''the Business.'' The Dwarfs are lesser powers (such as Honeywell and Control Data Corporation) that dare to do battle with the giant. Since the 1960s some of the original Dwarfs have retreated from the computer field, while other companies have joined the fray.

In fact, Fishman's book is less a fairy tale than a war epic - a blow-by-blow account of marketing strategies and counterstrategies, legal disputes, talent raids, and corporate infighting. Innovation in computer technology obviously plays an important role in the narrative, but abstruse jargon is avoided, and the focus is primarily on the business end.

Although a chapter on the antitrust suit against IBM was written before the federal government dropped its case, there is abundant information here to draw one's own conclusions as to its validity. Other chapters intelligently explore computer-related social issues (such as individual privacy) and likely computer applications of the future.

Despite the muckraking sound of the title, ''The Computer Establishment'' is balanced, thoughtful, and painstakingly researched (over a period of 10 years). A plethora of details may discourage the casual reader, but anyone with a more serious interest should find it absorbing.