DURING HIS almost 30-year career, John Barth has shown himself to be a master of a remarkable variety of literary forms: both the short and long novel, short fiction, the novella. Sections of verse (some burlesque, some not) are included in many of his fictions. A long rhymed-couplet play that delightfully parodies Oedipus Rex appears in Giles Goat- Boy. Recently he told an interviewer about a television script that he'd been working on.

What next? In The Friday Book, we learn that all along (since 1960 at any rate when he first began giving public lectures at various universities) he's also been intrigued by the essay form. His interest in nonfiction has become so strong indeed that, as he explains, he now makes room for it in his writing schedule. "Four mornings a week from September through May I have for some years been privileged to make up and set down my stories in a pleasant white house in the city of Baltimore, where in the afternoons I teach at the Johns Hopkins University. On normal Thursday evenings my wife and I drive across the Chesapeake Bay Bridge to a pleasant red house on Langford Creek, off the Chester River, off that same Bay, where on Friday mornings . . . I refresh my head with some sort of sentence making, preferably nonfiction." Hence the contents of this book and the significance of its title.

Those years of Fridays amount to an ample volume. In addition to three forewords and two chunky epigraphs ("Prefatory notes and other introductory material should be avoided wherever possible," Barth drolly remarks), there are 37 pieces about writing, philosophy, and esthetic theory collected here. Some are not so much essays as introductions to readings or remarks made by Barth while he served on literary panels. These are by definition short and undeveloped, though nonetheless fascinating. Many others, however, are essays -- long, elaborate, fully developed, and even more fascinating. With one exception (a 1982 autobiographical "Some Reasons Why I Tell the Stories I Tell the Way I Tell Them . . ."), the sections are arranged in the order of their composition, starting in 1960. Each has a headnote, often lengthy, that explains the circumstances under which it was written.

Several pieces have been published before -- Barth's much discussed, often misunderstood, hence controversial views on the state of modern fiction, "The Literature of Exhaustion" (1967), and what he describes as its corrective companion, "The Literature of Replenishment" (1980). A 1964 afterword to the Signet edition of Smollett's Roderick Random is included, as is a 1973 Penn State Festschrift essay on that frame tale of frame tales, The Ocean of Story. There are items from The New York Times Book Review, The Boston Globe, The Washington Post, and Esquire, not to mention less available sources. Devotees of Barth will be pleased to have these diverse items brought together and to rid their bookshelves of long-since wrinkled, yellowed clippings. Those coming new to Barth will have the pleasure of first acquaintance.

But even Barth's fans will encounter the unfamiliar, for many of these Friday-pieces have never been in print until now. Of these, an essay about Barth's most recent novel, Sabbatical, is a special pleasure. Another, "The Self in Fiction," has a dizzyingly-compact two-page backward summary of the history of literature. Yet another, the last and among the most enjoyable, proposes an ingenious, biological (might as well say fertile) explanation for Scheherazade's narrative (sexual?) strategy in saving her life by telling stories to her king for a thousand and one nights. Why that particular number? Barth asks. And what about those three children that she suddenly mentions at the end of the cycle?

These Friday-pieces have the qualities suggested by the metaphoric title of one of them, "Algebra and Fire." Skill and knowledge, technique and information -- they are the algebra. And the fire is passion -- for ideas, for literature, for words.

Whether discussing modernism, postmodernism, semiotics, Homer, Cervantes, Borges, blue crabs or osprey nests, Barth demonstrates an enthusiasm for the life of the mind, a joy in thinking (and in expressing those thoughts) that becomes contagious. Indeed, if you've ever wondered what modernism, postmodernism and semiotics mean, you've found the right place to learn. A reader leaves The Friday Book feeling intellectually fuller, verbally more adept, mentally stimulated, with algebra and fire of his own.