That was the problem: the Reading Room was and is sacrosanct. Logically, since it was now surplus to requirements, it should have been demolished. The whole courtyard could then have been cleared and covered - or perhaps filled with a new structure, though Paris had irritatingly nabbed the pyramid idea. As with the Louvre, the court holds the key to the whole museum. You go to the centre, and from there navigate north, south, east or west to whatever part of the museum you want. So much simpler than the dog-legged arrangement for getting around the place that will finally be laid to rest when the Great Court opens (just after a Sunday Times party there, as it happens). But no, the Reading Room had to remain, and it had to be a library with all its original shelves and radiating spokes of tables. It was not allowed to become a concourse. What to do? As an architect, Lord Foster is arguably at his best when dealing with recalcitrant historic buildings. He'd done it when he reinvented the heart of the Royal Academy, he'd even done it with the Reichstag in Berlin, for heaven's sake. And he knew what to do with the British Museum. Underneath the giant glass doughnut of his roof, he designed an egg.

The Reading Room, with its green copper dome rising through the new glass roof, is the yolk: a concourse of shops, cafes, and galleries is the surrounding white. Lecture theatres are dug out beneath it. This streamlined oval shape fits neatly into the restored courtyard and leaves plenty of open space for you to wander round and take short cuts from one side of the museum to the other. But Foster takes it further than that. The flanks of his limestone egg contain grand curving staircases that wrap round the Reading Room , taking you up to a restaurant terrace at the pointed end of the egg. From there, a new bridge takes you into the northern galleries of the museum at high level. It's a very clever way to - literally - get round the problem of a large immovable object.

As for the Reading Room itself, that is open to everyone for the first time ever. Previously, you had to be a registered reader in the library, one of the elite, distinctly superior to the hoi polloi surging like tidal waves through the galleries around you. The Reading Room now holds the Walter and Leonore Annenburg Centre - a modern library which combines multimedia computers (which let you find out more about objects in the museum) with the millionaire publisher Paul Hamlyn's collection of 25,000 cultural volumes, each selected for its bearing on the civilisations and societies that produced the artefacts in the museum's collections.

There have been a few glitches along the way. There was a bit of a brouhaha when claims were made that the new glass doughnut roof was higher than some people expected. And there was a real stink when it turned out that the new south portico into the Great Court - a grand classical entrance, drawing on the language of Smirke to replace a long-demolished original - was in a paler French limestone than the Portland stone of the original. That was a real mistake - the Museum says it was misled by its contractors - but it is also a real storm in a teacup. Some influential individuals have called for the portico to be pulled down and rebuilt. Poppycock. The stone colour difference is so slight as to be irrelevant. The portico is clearly new, its stonework sharply cut compared with the weathered and patched facades around it. Well, of course: it IS new. William Morris, the late Victorian arbiter of taste, had no truck with restorations that tried to pass themselves off as the original. "Honest repair" was his credo. And this is honest repair. Perhaps it should have been a modernist portico, but at least it is not a fake.