An engaging, handsomely full-dress, but oddly unrevealing biography of the unquestioned master of locked-room mysteries and impossible crimes. Carr (190677) was the most fascinating of the great detective writers, including Dorothy Sayers and Rex Stout, who flourished between the wars. Greene (History/Old Dominion Univ.), who has already edited four volumes of Carr's short stories and radio plays, accurately identifies the apparently incompatible elements the writer exploited in such genre classics as The Three Coffins and The Burning Court: ``supernatural atmosphere, fair- play detection, complex but lively narratives, uproarious comedy, and a romantic interest in the past and in Adventure in the Grand Manner.'' Greene shines as a bibliographer; anyone who has tried to bring order to Carr's prodigious output will be grateful to him. But although he can trenchantly summarize individual habits of mind (on his subject's conservatism, for instance: ``Carr almost never objected to a social structure''), Greene never succeeds in resolving, or even in satisfyingly exploring, the contradictions of Carr's personality, by turns punctilious and devil-may-care, or the simultaneously florid and analytically precise nature of his stories. And Greene's copious criticism of the novels and tales accepts Carr's own standards of judgment- -which emphasize above all liveliness and the conscientious placement of clues--so completely that, though his judgments of relative merit are apt, they are never more acute than the author's own. The major biographical revelations here--Carr's periodic drinking and wenching, the influence of his accomplished radio plays (``probably the best mystery dramas ever created for the radio'') on his inferior later novels, the stroke he tried to keep from his public in 1963--will come as no surprise to knowledgeable fans. Carr's legion of readers will know better than to expect any major new critical or biographical insights from this entertaining five-course feast of the familiar.