Commanding the plateau of al-Sabika above Granada, with the snowy summits of the Sierra Nevada looming majestically behind, the Alhambra is not only the supreme artifact of the waning culture of Muslim Spain but one of the enduring constructs of the human imagination as well. For every established fact of its history and design there are, it seems, a thousand fantasies. Like the Pantheon or the Taj Mahal, the Alhambra is one of those archetypal and fabulous structures where fancy loves to dwell. Had Jorge Luis Borges been an architect, he would have built structures akin to this fragile and ambiguous complex. Like his Library of Babel, the Alhambra is at once a site of inexhaustible nuance and a glittering mirror of the cosmos; it is profusion crystallized, abundance subject to exactitude, a kind of encapsulated infinity.

The name comes from the Arabic word al-hamra’, meaning “red,” but this may denote less redness in the literal sense as much as regal splendor. (After all, Fez and Marrakesh – both important coordinates in the Muslim Andalusian culture that held sway in Spain for some 700 years – are known respectively as the “green” and the “red” cities, not for the predominant colors of their tiles and stones but for the hieratic associations of these hues.) Like the site, the name itself is old, attested as early as the ninth century, though the palace complex we know today had its origins after 1238, when the Nasrid ruler Muhammad Ibn al-Ahmar ordered its construction. This was to be no mere pleasure palace but a seat of government, containing offices, barracks, audience halls, royal residences and council rooms, as well as such public amenities as a mosque, baths, artisans’ quarters, and shops.

Much of the mystery and the complexity of the Alhambra, as we see it today, is the result of successive accretions; few sites have been so added to, re-conformed, patched up, restored and, yes, falsified, as the Alhambra. Certain of these additions, such as the palace of Charles V, built after 1526, did not supplant the Muslim structure but stood beside it; thereby, in the words of the Spanish scholar Emilio Garcia Gomez, “affording the delicate old cheek of the Alhambra a cushion of stone to lean against.” Others, however, especially the “restorations” by modern architects, have disfigured or betrayed the spirit of the buildings. Add to this the many remaining puzzles and questions about the history of Muslim Spain in its final years – the record is woefully incomplete – and the necessity for a reliable and accurate guide to the Alhambra is immediately apparent. Sad to say, most available guides are worthless.

The English historian and novelist Robert Irwin has provided a remedy. He has a rare knack for untangling knots and threading labyrinths. In his “The Arabian Nights: A Companion” (1994, but still available in paperback), he unravelled the many textual and historical puzzles of that fabulous compilation with clarity and insight. His new “The Alhambra” (Harvard University Press, 224 pages, $19.95) is a succinct, witty, often acerbic compendium of facts, legends, and outright delusions about this Nasrid architectural masterpiece. He also manages, with style and flair, to convey a surprisingly rich store of detail on medieval Andalusian culture and life. His choice of illustrations, some 21 in all, complements the text superbly. My only complaint is that the plan of the Alhambra given at the outset is not keyed conveniently enough to the narrative.

Beginning with a collation of the many errors and misconceptions about the Alhambra, some of which makes hilarious reading, Mr. Irwin guides the reader through the complex itself from the Alcazaba and the Court of the Myrtles to the Court of the Lions and “the Alhambra of the Christian Kings.” He is the ideal companion: amusing, learned, curious, often eloquent. There are wonderful digressions. For example, he notes that Columbus witnessed the fall of Granada in 1492 and that when he set sail for the Indies in the same year, he took with him Luis de Torres, an Arabic-speaking Jew; after they landed in Cuba, thinking it was Japan, Torres proceeded “to address the mystified Tainos natives in Arabic.” The book abounds with such bizarre and comical anecdotes.

Even better, “The Alhambra” contains much precious detail drawn from the Arabic sources, historical as well as literary. Mr. Irwin trained as an Arabist and is well equipped to offer his own translations of poems and chronicles and to speculate on many of the linguistic riddles the various rooms and features of the palace offer. Sometimes these are small but telling details. He notes, for example, “that medieval Muslim princes spent huge sums on vast candles – a specialty of medieval Damascus. The palaces of the Alhambra all seem to have been lit from below. Ibn al-Khatib, the Nasrid vizier and court poet, writing about the 1362 festivities to mark the Prophet’s birthday, remarked on the ‘standing candelabras of bronze and glass with wide bases, thick stems and many pendant candle-sockets.’ “

The same Ibn al-Khatib quoted above is one of the heroes of the book. Born in 1313, he exerted considerable influence on the subtle designs of the Alhambra. A polymath, he excelled not only in poetry and mystical philosophy but even wrote on medicine and, as Mr. Irwin notes, argued that the plague of 1349 was caused not by divine fiat but by contagion.

As vizier to the Nasrid ruler Muhammad V, Ibn al-Khatib followed his prince into exile in Morocco in 1359 and returned with him to Spain in 1362, deeply affected, it appears, not only by what he had witnessed in Morocco but by his profound immersion in Sufi meditation and practice. The fervent doctrine of divine love promulgated in the treatises of the mystical genius (and fellow Andalusian) Ibn ‘Arabi marked Ibn al-Khatib and, Mr. Irwin suggests, seems to have found expression in certain aspects of the intricate geometric designs of the Alhambra. Ibn ‘Arabi espoused an extreme monism, usually termed “the oneness of being,” and this may be incorporated and reflected in such details as the endlessly interlooping designs of tiles and stalactite ceilings where the “one and the many” appear as simultaneously plural and unified.

Despite his gifts and his powerful connections, Ibn al-Khatib, like all viziers, came to a bad end. Brought up on a contrived charge of heresy, he was jailed in Fez. There he penned the moving verse: “We used to feed others, but lo, now we are food for worms.” In 1375, still awaiting trial, he was strangled by a “special execution squad from Granada.” His body was later disinterred and burned by his implacable enemies, earning the hapless fallen vizier the sobriquet “the man of two deaths.”

Mr. Irwin contrasts this quick but compelling sketch with another, this time of Ibn Zamrak, Ibn al-Khatib’s successor and rival, many of whose verses embellish the walls of the Alhambra. Fittingly enough, Ibn Zam rak ended up as the victim of another execution squad, who “found Ibn Zamrak at home reading the Koran and slaughtered him and his two sons in front of his wives and daughters.” These and other episodes reinforce Mr. Irwin’s contention that the Alhambra in fact was a “poisoned paradise.” (It’s worth noting that the sultans themselves didn’t fare any better than their viziers: of the nine Nasrid Sultans, seven were murdered, one died accidentally, and only one had a natural death.)

Such details give a salutary bite to the otherwise sugary confection various writers and travellers, from Washington Irving on, have spun of the Alhambra. Mr. Irwin has a way with the telling citation. Thus, he quotes the 19th century traveller Richard Ford on the famous lions of the Alhambra: their “faces are barbecued, and their manes cut like scales of a griffin, and their legs like bedposts, while a water-pipe stuck in their mouths does not add to their dignity.” (Ruskin and Gerald Brenan are among the other writers distinctly unenchanted by the Alhambra whom Mr. Irwin quotes.)

The best and most interesting pages are on the deeper significance and function of the Alhambra. Mr. Irwin frames the question in this way: “The beauty of the Alhambra is based upon proportion and upon abstract geometric designs of staggering complexity. What did the educated medieval Arab see when he gazed on those patterns?” To answer this question, he provides a pithy but wide-ranging discussion not solely of the views of contemporary art historians and scholars of the Alhambra but delves into earlier philosophical and mystical cogitations, ranging from Pythagoras and his followers to the enigmatic group of 10th-century thinkers known as the “Pure Brethren of Basra,” from whose encyclopedic “Epistles” he cites. His argument is that “the Alhambra was designed by and for intellectuals with mystical inclinations. It was a machine for thinking in.” This is, needless to say, not the standard view, but Mr. Irwin makes a compelling and convincing case for his thesis.

The Alhambra has an appearance of impregnability and yet it is the most fragile of structures. When Ferdinand and Isabella took Granada in January of 1492, the Alhambra capitulated without a struggle. That strange melange of the precarious and the monumental led Emilio Garcia Gomez, whom I cited earlier, to describe the whole dazzling structure of the Alhambra as “a palace on four stilts.” If he is right, then Robert Irwin has now succeeded in showing us the historical and the metaphysical supports upon which this most precise of architectural fantasies rests.