Everything I admired about the new Ashmolean museum is symbolised by the reopening of the massive front doors under the central portico of Sir Charles Cockerell's 1845 neoclassical building. They have long been closed, forcing visitors to use a far less imposing entrance at the side. Whereas the entrance hall used to lead to tenebrous galleries lined with antique sarcophagi, now it opens on to the light-filled atrium of the new extension, and whereas the old (and much loved) galleries were shabby and stuffed with works of art, the new ones are sleek and spacious. 

The architect Rick Mather has left the wonderful Cockerell building intact, but audaciously replaced the undistinguished late Victorian galleries at the rear with a six-storey building that adds 34 new galleries and four new spaces for temporary exhibitions - effectively doubling the size of the old museum. In addition to what the public sees, the Ashmolean has a new conservation studio, and an education centre which, considering it's function as a teaching museum in the heart of Oxford, amazes me didn't exist before.

In a conventional museum design each of the six levels would be given over to contiguous gallery spaces lit by a mixture of natural and artificial light and connected vertically by stairs and lifts. But the new extension is surrounded by buildings on three sides, so glass walls or windows weren't ideal ways to let light in. And without natural light you'd have ended up with a stack of claustrophobic boxes. Mather found an ingenious solution to the problem by putting a glass roof over the central space, and then eliminating the floors and ceilings on all the levels directly under it to create an 80-foot atrium.

On either side of it, double height galleries for major displays alternate with subsidiary galleries with lower ceilings. At the centre, where floors and ceilings have been whisked away to let the light in, elegant steel and glass bridges connect one part of the building to another.

One of the joys of the design is crossing these bridges and looking on to a dramatic display of Islamic art in the gallery below, or else across to the musical instrument gallery, which you glimpse through an interior wall pierced with glass. In the use of these vertiginous vistas and in the dramatic diagonals of the staircase, the soaring central space feels as though it was inspired by Piranesi.

The galleries are quirky and unpredictable, full of nooks and crannies and yet completely navigable even to the dyspraxically challenged, like me. That's as much to do with the layout by the exhibition designers Metaphor as with the architecture. At entrance level, for example, you find galleries devoted to Greek and Roman Sculpture, the Ancient Near East, and the Aegean world on one side of the atrium, with ancient India and China on the other.

One flight up, you start with the Fall of Rome and end with the Late Middle Ages. More than 400 new display cases, many of which are floor-to-ceiling and set into the walls so that the exhibits can be seen from both sides, serve the objects well. The lighting, though unfinished when I visited, is high tech.

As for labelling and presentation: for the display of a permanent collection I dislike themed galleries with didactic wall labels. I guess they are OK for children, but they limit both the curator's ability reconfigure the display and the viewer's capacity to interact with the objects without being told what to think. So, themed displays like East Meets West waste almost as much space as the dreadful Welcome Galleries at the British Museum.

On the other hand, some of these thematic wall labels are so banal that they really can't be accused of telling anyone anything. Here's an example: "The ancient world was inhabited by diverse people living through the vast and varied terrain of Europe, Asia and North Africa. There were many differences between these people yet there were also connections." Since my eighth birthday came and went some time ago, explanations like these don't tell me anything I didn't know. I must quickly add that elsewhere are strange and wonderful galleries dedicated to old fashioned displays of the Meiji period in Japan, tin-glazed ceramics and medieval Islamic textiles. Much of this material has never been on view before, simply because the Ashmolean had no place to show it.

The collections I know best at the Ashmolean are of European painting and sculpture. These are still shown in the old Cockerell galleries, which have been given new floors, skylights, wall coverings and lighting - making old favourites like Paolo Uccello's The Hunt, Nicolas Poussin's The Exposition of Moses, Giovanni Paolo Panini's View of the Piazza del Popolo and my favourite dog in art, a mutt by an anonymous Genoese artist, look better than they ever have. Recent acquisitions like Titian's Triumph of Love, a superb roundel showing Love conquering all in the form of cupid riding on the back of a ferocious lion, add oomph to a collection that, although wonderful, doesn't really have the show-stoppers you find at the Wallace, Dulwich, or the National Gallery.

An interior corridor hung with the Gere collection of plein air landscapes sketches looks superb. interspersed with works from the Ashmolean's collection, such as the limpidly beautiful Corot from the mid-1820s, Lago di Piediluco, Umbria, and an enchanting little late Whistler oil on panel, showing the Shore, Pourville. And upstairs, you'll still find the Ashmolean's first rate collection of Pre-Raphaelite painting, the Pissarros, and a recent, exceptionally important bequest of Sickert's from the family of the artist's pupil Ethel Sands.

But the point of this review is not to take you on a gallery by gallery tour of the collections, merely to report on the success of this project and to congratulate Rick Mather and the director Christopher Brown on their £61 million achievement.

It is money well spent.

Richard Dorment
Daily Telegraph