A Rose by any other name; The Name of the Rose, by Umberto Eco. Translated from the Italian by William Weaver. San Diego: Harcourt Brace Jovanovich/A Helen and Kurt Wolff Book. 502 pp. $15.95.

How might we explain the best-selling success of a novel by an Italian academic set in a medieval abbey where the focus of monastic life (along with prayer) is the preservation of a vast library? What fascination might the theological and political disputes of the 14th century hold for the 20th-century reader - the rivalries between Pope and emperor, bishops and abbots, between reformist friars who preach poverty and wealthy clerics who support the church's claims to property? Is all this palatable only because it is part of an ingenious detective story in which a Sherlock Holmesian English friar, aptly named Brother William of Baskerville, assisted by a naive young monk called Adso , solves the puzzle of a series of lurid and mysterious deaths?

Mysteries, to be sure, are always popular, in large part because they deal with the emotionally charged topics of crime and violence. ''The Name of the Rose'' is no exception. The story unfolds in an atmosphere thick with hostility and intrigue. What the great medieval historian Huizinga called the mingled odor of blood and roses is in the air, with the emphasis on the blood. Innocent people are being burned as witches and heretics. And the corpses of monks keep turning up when least expected. It would certainly be impossible to accuse Eco of having written a dry academic novel.

But mysteries also draw their appeal from another source, the basic reason we read at all: the desire to find out, to discover explanations for the unexplained, to search out meaning. Linguists and semioticians remind us that reading itself - from the primary act of deciphering letters and words to the final act of interpreting what we've read - is like solving a mystery by piecing together signs and clues. Who better, perhaps, to write a detective story than a semiotician like Umberto Eco - a theorist and practitioner of the abstruse academic art that studies signs and meanings?

In this story, the detective is both practitioner and theorist: He must not only solve the mystery, but must also explain his newfangled method of trial and error to his young assistant, whose more traditional training has taught him that one reasons by starting with a universal truth, deriving individual cases from unchallenged axioms, not by inventing and then testing a series of dubious hypotheses.

Objects, as Eco the semiotician points out, can function as signs. William's spectacles signify the knowledge and experimentation that went into their making and the sharpness of vision their wearer strives for. Merely to possess knowledge is not enough, William feels: One must learn to see and think with greater clarity and flexibility. Yet to Adso, and to others still more steeped than he in medieval tradition, nothing can be clearer than the absolute truth of authority.

For many of us, heirs of the Enlightenment, the process by which we formulate and test hypotheses seems ''only natural.'' It is anything but. By setting his story at a time when other forms of thought prevailed, Eco re-creates a sense of the difficulty and challenge of a method we take for granted.

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