NONFICTION

Ernest Hemingway and His World, by Anthony Burgess (Scribners, $10.95). In this handsomely illustrated biography, Anthony Burgess gives us a look at Hemingway the social creature. His perigrinations took him all over Europe and America, to Africa and the Caribbean. His life intersected the lives of Americans abroad -- Scott Fitzgerald, the Murphys, Gertrude Stein. and his associations included those with movie stars (Ava Gardner, Ingrid Bergman) and revolutionaries (Castro). His world, in short, was richly varied and liberally populated with the rich and famous. And Burgess tells the tale gracefully in this slim, informative book.

Hardy: A Biography, by Michael Millgate (Oxford, $13.95). When Thomas Hardy was buried in Westminster Abbey in January 1928 he was the first British novelist so honored since Dickens and the first poet since Tennyson. If his reputation was high at the end of a very long life (he was born in 1840), it is no less so today. This outstanding biography is noted for its command of the documentary sources of the life and its sympathetic view of Hardy the man. It relates with extraordinary sensitivity the ways in which his artistic interests were deeply rooted in a personal and very local past, and why this first of the "modern" novelists chronicled so thoroughly the revolutionary changes that swept over the English countryside in the 19th century.

A Savage War of Peace: Algeria, 1954-1962, by Alistair Horne (Penguin, $6.95). In France's long effort to stifle rebellion in Algeria, six prime ministers fell, the Fourth Republic collapsed, DeGaulle was summoned to power, a million Muslim Algerians were killed, and a million French colonists were forced to emigrate. It was a conflict marked by unimaginable savagery on both sides, and its history is here brilliantly and compasionately told by an historian whose mastery of his subject is complete.

The Last Laugh: The World of the Stand-Up Comics, by Phil Berger (Limelight, $10.95). A hard- boiled, frequently raunchy tour of the smoky night clubs and sweaty cabarets where two generations of American comedians polished their lines. Among the many artists covered are Henny Youngman, Milton Berle, Mort Sahl, Dick Gregory, Woody Allen, Bill Cosby, Lily Tomlin, Cheech & Chong, Rodney Dangerfield and Eddie Murphy. If you can't stand the zaniness, stay out of the fun house.

Tolstoy or Dostoevsky: An Essay in the Old Criticism by George Steiner (University of Chicago Press, $12.95). One of the meanings of critic Steiner's subtitle is that he is not a relativist. Citing with nostalgia Matthew Arnold's olympian judgment that Homer is "one of the five or six supreme poets of the world," he adds a verdict of his own: Tolstoy and Dostoevsky are the world's two greatest novelists. Few would quarrel with giving the laurel to Tolstoy. It is in his argument for according Dostoyevky comparable status that Steiner comes into his own. He justifies what bothers modern readers most about the author of The Brothers Karamozov -- his sensationalism -- by noting that Dostoyevsky was trying to portray "the anguish of the day" in a manner that avoided what he saw as the blandness of Turgenev and the archaism of Tolstoy -- while at the same time realizing that Russian literature lacks the tragic tradition available to English writers. The result was that he borrowed the conventions of Russian melodrama and recast them in his own mold. Steiner's long, leisurely study is literary criticism at its finest. MYSTERY AND SUSPENSE

The Fifth Angel, by David Wiltse (Pocket, $3.95). A killer on the loose -- the theme sounds hackneyed, but David Wiltse has wrought some changes in it. This killer is a pro, a trained commando who is buried alive by accident during a war game. When he extricates himself, three days later, he is a maddened instrument of death who finds his niche in the sewers of New York City. The book is another literate thriller by the author of The Wedding Guest.

Death in a Cold Climate, by Robert Barnard (Dell, $3.50). For many years Robert Barnard, one of the most best English mystery writers, taught English at the University of Tromso, Norway, three degrees north of the Arctic Circle. As its title indicates, this mystery capitalizes on that setting. It begins with a dog uncovering a naked corpse in the snow and ends under the midnight sun. In between are the customary elements of a Barnard book: fine characterization, stylish prose, and full-bodied background, as in this description of nerves wearing thin as winter lengthens and lengthens some more. "As March shaded into April, the elements played coy games with the North Norwegians. Some days they flattered them with hopes of an early pring: the roads were clear, and there was the pleasure of walking on nature's own tarmac again. . . . These were the days of delusion. Next day the skies would be angry grey and lowering, the snow would fall, and by nightfall nature white in tooth and claw had reasserted is accustomed iron rule."

Green Ice; Death in a Bowl; The Virgin Kills, all by Raoul Whitfield (Quill/Mysterious Classic, $3.95 each). There was a time, not so long ago, when the only hard-boiled American fiction in print carried the names Hammett, Chandler or Cain. But during the past decade paperback houses have reissued tough- guy classics such as Paul Cain's Fast One, the novels of Jim Thompson and Cornell Woolrich, and the Parker books of Richard Stark (aka Donald E. Westlake). Raoul Whitfield's three novels are firmly in the Hammett mode, and the creator of Sam Spade himself blurbs Green Ice, forgoing his characteristic understatement, as 280 pages of "naked action pounded into tough compactness by staccao, hammerlike writing." Most modern critics think Death in a Bowl a better novel, the investigation into the murder of an orchestra conductor at the Hollywood Bowl, with suspects drawn from the usual L.A. repertory company: the fading movie star, neurotic director, artsy screen writer.

Rim of the Pit, by Hake Talbot (International Polygonics, $4.95); The Emperor's Snuff Box, by John Dickson Carr (Carroll & Graf, $3.50). Aficionados of problems derived from the hermetically sealed chamber -- aka the locked room mystery -- rejoice! Here are two masterworks of the genre: Hake Talbot may sound like a hard-boiled gumshoe but his puzzle deftly blends the seemingly supernatural with ingenious deduction. John Dickson Carr himself acclaimed it a classic, and there can be no higher praise than that. The master's own touch is demonstrated in this latest Carroll & Graf reissue, its only drawback that it features neither Sir Henry Merrivale nor Dr. Gideon Fell.