There is a sticky moment for anyone associated with this Magazine when they begin a visit to the newly extended and redisplayed Ashmolean Museum in Oxford. In an introductory section to the collections in the lower ground-floor galleries, a showcase on fakes and forgeries contains an attractive silver reliquary head. The accompanying label notes that the head was published in the Burlington in 1919 as an Italian piece dating to the 1100s. Then owned by the prominent collector Henry Harris, it was subsequently acquired by the Ashmolean, where it was later discovered to be of composition metal only possible after c1800. This nice example of the triumph of technical analysis over connoisseurship immediately puts visitors on their mettle. It and its surrounding tasters on conservation, the Museum's history and 'Exploring the Past' make quite clear the multilayered nature of the new display of the Museum's holdings, all coming under the capacious if somewhat anodyne heading 'Crossing Cultures Crossing Time'.

But first the building itself must be applauded. There is no doubt that the transformed Ashmolean is a major addition to the changing landscape of museums in Britain. The architect of the extension, Rick Mather, has provided a beautiful and ingenious solution to a difficult site. Behind the imposing porticoed building of 1845 by Charles Cockerell, all later additions have been demolished to make way for thirty-nine new galleries on five levels, as well as many of the services expected of an up-to-date museum, such as an education centre and new conservation studios. A great bonus is the new glass entrance under the portico, the only feature that announces changes have taken place (for the new building is invisible from the street). A few paces straight ahead and one is in Mather territory rather than Cockerell's. Two finely detailed, easily negotiable staircases run between the floors, offering intriguing views of the galleries at every stage. Although the new addition has no facades of its own, hemmed in, as it is, by earlier buildings, there is no sense of claustrophobia; all is light and airy. The galleries vary greatly in size and form - from extended treasure trove to the small and intimate - all with their own personalised lighting. Many of Cockerell's older galleries - predominantly those given over to European painting - have been refurbished; one moves effortlessly between old and new, from upholstered familiarity to reassuring moderne.

One or two commentators, with a just perceptible hint of criticism, have characterised the new building as 'polite'. This is true - and is a great strength. Cockerell's venerable edifice, like an imperious stage duchess turning a blind eye to life on Beaumont Street and the upstart Neo-Gothic of the Randolph Hotel, needed respect and politesse from a sprightly heir, hard on her heels. This Mather has shown admirably with neither fawning emulation nor a desire to shock. He is perhaps a shade restless but this can add to the excitement of discovery. The Ashmolean's extraordinarily varied collections of art and archaeology, founded as they were on the Tradescants' hoard of curiosities, had need of a building that could internally accommodate this variety - from coins and clothes to pots and paintings - within a coherent concept of display. This is not a building into which a museum's holdings have simply been decanted. The exhibition design firm Metaphor has developed the 'innovative display strategy', basing it on the idea that, across the centuries, cultures have overlapped and interacted. We are therefore on the somewhat stale ground of contemporary multiculturalism. What is perhaps new is the relative lack of emphasis on the religious dimension (although this is often taken care of on individual labels) and the playing down of formal and aesthetic connections in favour of materials and utility, trading routes and diplomatic exchange. Within its own terms it has been thoroughly thought through, with all curatorial hands on deck. The historic departmental divisions of the Ashmolean are interwoven in a story that is essentially material-based, culturally omnivorous and fully contextualised. Most of the works on show are anonymous - from modest craftsmen to obviously highly sophisticated but nameless artists. The textile collection is revealed for the first time; there are superb displays of Islamic and Chinese art, ceramics above all; tribute is paid to Ancient and Medieval Cyprus and India is comprehensibly visible (but there is virtually nothing on the civilisations of the Americas; travel is always East from Western Europe). By the third floor we are in the Renaissance; we whizz through Japan; there is an innovative room on Britain and Italy. But somewhere here might there not have been one especially prepared room for a selection from the Museum's great collection of works on paper? Access to the Western Art Print Room is available only by request.

Through many of these galleries runs a subtext that draws attention to the Museum's history and benefactors and to the archaeologists responsible for unearthing so much that has come to rest in Oxford. Interesting as all this is, it can be distracting, breaking the spell of the objects themselves, already abundant and fully (if sometimes banally) labelled. Perhaps one room dedicated to this unpicking of the Museum's history would have been sufficient. On the penultimate level (below a rooftop restaurant) we reach the nineteenth and twentieth centuries, predominantly showing paintings. Here, jumps in chronology and school are erratic - the paintings collection of the Ashmolean, unlike its drawings, is not one of its glories. The emphatic contextualisation controlling the earlier displays eases off, as though Metaphor and the curators had run out of breath. Mather the focused rooms on the Pre-Raphaelites, the Pissarro family and Sickert and his contemporaries, the gallery devoted to modern art is perfunctory and miscellaneous. More substantial works are needed here to quicken the pulse and end on a higher note. Four new, currently empty galleries for temporary exhibitions will come into their own later in the year. But what a relief it is to find no interventions by contemporary artists, no celebrity names to distract us from one of the greatest of all cabinets of curiosities now in its splendid new setting.