Alice Through the Needle's Eye, by Gilbert Adair. With Illustrations by Jenny Thorne. New York: Obelisk/ Dutton. 186 pp. $7.95. Further adventures of Lewis Carroll's ``Alice''? This engaging sequel takes that inquisitive young girl through the eye of a needle she's been trying - unsuccessfully - to thread, and into a land of puns, poems, talking animals, and figures of speech that turn into figures who speak! Gilbert Adair has something of that curious blend of sophistication and naivet'e, ingenuity and ingenuousness, that made Lewis Carroll so appealing. Anyone who's wished there were more of ``Alice,'' indeed, anyone who appreciates the logic of nonsense and the charms of wordplay, may well enjoy this clever, amusingly illustrated book. ------------------------------------------------------------------------------- A History of Religious Ideas, by Mircea Eliade. Volume 3: From Muhammad to the Age of Reforms. Translated from the French by Alf Hiltebeitel and Diane Apostolos-Cappadona. Chicago and London: University of Chicago Press. 360 pp. $16.95.

Romanian-born Mircea Eliade (1907-86) was a pioneer in modern religious studies, mapping out the terra incognita of archaic religions and occult practices and shedding light on the history of religion in general. The first two volumes of his ``History of Religious Ideas'' took readers ``From the Stone Age to the Eleusinian Mysteries'' and ``From Gautama Buddha to the Triumph of Christianity.'' This volume is apparently the last, although its preface indicates Eliade had hoped to write another presenting the traditional religions of Africa, America, and Oceania.

Although Volume 3 focuses on the period from the early Middle Ages to the Reformation, it looks back toward the shamanistic religions of ancient Eurasia and rabbinic Judaism in Roman times, forward as far as the Hasidic movement of the 18th century, and as far afield as Tibetan religion. This history highlights those ideas and persons that became part of the mainstream (Origen, Augustine, Muhammad, Maimonides, Averro"es, Luther), as well as heretical and schismatic cults and movements that also have their place in the pattern. ------------------------------------------------------------------------------- The Passion of Ayn Rand, by Barbara Branden. New York: Anchor Press/ Doubleday. 442 pp. Illustrated. $12.95.

Ayn Rand (1905-82) joyfully left her native Russia for America in 1926, discarding her old name (Alice Rosenbaum), taking her new name from a Finnish writer whose work she hadn't read (``Ayn'') and from a typewriter (Remington ``Rand''). The author of such novels as ``We the Living,'' ``The Fountainhead,'' and ``Atlas Shrugged,'' Rand championed individualism, free enterprise, and capitalism to such an extent as to denounce altruism as dishonesty and give selfishness the title of virtue. Her ``philosophy,'' rather misleadingly named ``Objectivism,'' found admirers as diverse as Alan Greenspan, Raquel Welch, and Rock Hudson. It also influenced the libertarian movement, economic supply-siders, and devotees of a return to the gold standard. Her ideas, which struck the eminent philosopher Sidney Hook as a ``unique combination of tautology and extravagant absurdity,'' impressed her disciples as internally consistent and bold.

Passionate, intense, and, in a primitive way, brilliant, she was scornful of emotionalism, loudly dedicated to ``logic,'' prone to hero worship. She demanded a kind of worship from her followers. Barbara Branden (author of this biography) and her husband, Nathaniel, were disciples and close friends of Ayn Rand and her husband, Frank O'Connor. Ayn co-opted Nathaniel as her soulmate and lover, expecting - and pretty much receiving - Barbara and Frank's acquiescence. The most remarkable feature of this biography is the way Branden manages to tell the portion of Ayn's story involving this affair: with a fine indignation that never degenerates into recrimination. Branden's anger, like her admiration, becomes a tool in painting Rand's portrait, a key to understanding the contradictions of her character. ------------------------------------------------------------------------------- Place-Names of the World: A Dictionary of their Origins and Backgrounds, by Adrian Room. North Ryde, NSW, Australia: Angus & Robertson, dist. by Salem House, Topsfield, Mass. 259 pp. $12.95.

The act of naming helps provide a sense of place. Place-names may reflect geography (Dublin from dubh + linn = black lake, similar to the English Blackpool; Piedmont from pie de monte = foot of the mountain), or commemorate founders and other figures (Hudson, Houston, Wellington), or symbolize an ideal (Thailand from Prathet Thai = country of the free). Many, including Paris, London, Berlin, Spain, are shrouded in the mists of time or conflicting theories. This dictionary of place-names offers an intriguing international selection. Individual entries (more than 1,000) are well researched and succinctly presented. There is a good introduction, a bibliography, a guide to the ancient languages from which many of the names take their roots, and a list of non-English place-name elements (island, harbor, mountain, town, village, river, recur in many languages). ------------------------------------------------------------------------------- Ballet and Modern Dance, by Susan Au. Introduction by Selma Jeanne Cohen. London: Thames & Hudson, dist. by Norton, New York. 216 pp. Illustrated. $9.95.

From the court ballets and masques of the 16th and 17th centuries to the experiments of the 1980s, this carefully researched, thoughtfully written book surveys the history of theatrical dance. It is richly detailed, yet alive to the broader trends, both in dance and in the larger culture of which it is a part. Much attention is paid not only to famous dancers and choreographers, but also to composers, designers, patrons, and others involved in the world of dance, and there is a good discussion of the once-divided, now intermingling streams of ballet and modern dance. The text is profusely illustrated.

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