''The American Century: Varieties Of Culture In Modern Times''

----------------------------------------------------------------- "The American Century: Varieties of Culture in Modern Times" by Norman F. Cantor HarperCollins, $32.50 -----------------------------------------------------------------

As the 20th century comes down to the bottom of the ninth, and we have but three outs left, it's perhaps instructive to recall not only what the score is but who scored - and how.

In "The American Century," Norman F. Cantor, a professor of history, sociology and comparative history at New York University, has assembled an intellectual manual to our century. Used to trimming earlier times down to size in such works as "The Civilization of the Middle Ages" and "Medieval Lives," Cantor now makes tough, solid sense of our contemporary age. A copy of "The American Century" will be in the backpacks of next century's grad students.

He writes boldly about nearly everything modern and postmodern. You catch on quickly about psychoanalysis, phenomenology and deconstruction, for example, and encounter intellects such as Freud, Heidegger and Derrida. Cantor doesn't shy from assessing those who have made history or from provoking those living through it.

A combination of Will Durant and Voltaire, he exposes the game the way a learned scholar and a philosophical wit might team up in the press box not only to call the play-by-play but also to evaluate the opponents' money, marketing and mystique. His acid accuracy

burns through unexamined notions and succinctly reveals the ulterior implications of politics, both left and right.

This riveting summary of our era is supplemented by 48 pages of photographs of 20th-century art, shot by Mindy Cantor, the author's wife.