Apollinaire was a bizarre bundle of mystery and mishap; the darling of the ubists, Dadaists and Surrealists (he invented the term), he was also a Russian- Polish love child whose father may have been the great-grandson of Napoleon; he was also- mistakenly- the ""only person arrested in France for the theft of the Mona isa""; he fought at Verdun, won the Croix de Guerre and died a war hero two days after the Armistice. And he was, of course, a poet. All these and many other sides of Apollinaire's slippery persona Francis Steegmuller's sleek study commemorates. It even clears up- at least on these shores- some of the clutter: Picasso id ""betray"" Apollinaire vis a vis the Louvre bit; Annie, his Rhine muse, never surrendered to him and until recently never knew that the boy she rejected became to famous they named a street after him in Paris. On Apollinaire as a pioneering oet, Steegmuller's slight, but he offers a crackling account of his less than enetrating propagandizing for the Cubist cause and his Villonesque Left Bank life with Braque, Jacob, Derain, Picasso. Besides Maman, a loose-living one-time aristocrat, and Annie, Apollinaire's women were the painter Marie Laurencin (""a feminine version of myself"" said Apollinaire, ""destined to make men suffer""; she did: him), The Comtesse ""Lou"", Madeleine, and Jacqueline, the girl he finally married. He ang of them all in his poems, from Alcools to Calligrammes. Apollinaire's prison hay, his letters from the battlefield and the trepanation of his head are minutely, ovingly shown. In general, biographers have never had a smashing success with Apollinaire's somewhat self-mystifying life; Steegmuller almost changes that score.