For this its sponsoring council, the increasingly design-aware borough of Southwark, deserves praise. For the library is the latest piece in a new civic square laid out by the council on the long-lost terminus of a short canal leading to the Surrey Docks - now a green, linear park. The water should have been kept - what an asset to throw away in the parched inner city- but the new generation at Southwark has gone some way to atone for the mistake of its predecessors. After all, they could have allowed yet another superstore or multiplex cinema or dumb office complex or flats development here, for easy money: but they chose a more public-minded solution instead, on the back of government regeneration money granted to rebuild some notorious nearby housing estates. The first piece in this new space was an intriguing broad entrance archway, contributed by the young architect John McAslan a few years back as a statement of intent. A rather nondescript health club designed by the borough's architects then followed on one side, but the true ambition of the scheme only became apparent when Alsop was invited to design the library to face it.

At first glance, you might be forgiven for thinking that Alsop's library is an entirely arbitrary form, or one that could contain almost any activity. To an extent this is true. His working methods tend to be more those of the artist than the architect, and he would have you believe that his architecture tends to emerge from dribbly watercolours: design from the outside in, rather than - as is always the purist modern way - from the inside out. Alsop likes buildings on stilts, that start a long way up in the air and allow landscape to flow beneath. He also likes buildings that suddenly shoot off at right angles to themselves, and which contain sundry mysterious organic-shaped pods. He has explored these themes for years, mostly in unbuilt work such as - very appositely - an abandoned earlier scheme for a literary centre, a modern athenaeum, in Swansea. But is there anything in the Peckham scheme that is specific to the idea of being a library, as opposed to an office building or apartment block?

I suspect not. I think we can dismiss any fanciful notion that the shape is a bit like an open book, just in case anyone should think of suggesting that. But what I do know is that, having toured the red-carpeted interior, this building is going to work beautifully as a library, despite or maybe because of the inclusion of some modish other functions. Its narrow stem contains a suitably lofty entrance hall, with a local council office ("one-stop shop" in today's jargon) to one side. The next level brings you to an educational bit and some more jargon: an "open learning centre", whatever that means. But then you emerge onto the tall top floor housing the library proper, set in the cross-stroke of the L: and this is a fine space indeed. Not just for its views, though they are carefully considered: one window, for instance, eccentrically frames just a patch of sky, like something by the artist James Turrell. Not just for its exemplary indirect daylighting, which puts Alsop and his project director Christophe Egret on the list of architects indebted to John Soane , the Georgian master of the well-lit interior. No, there is something else, an appropriate sense of order and calm mingled with a dash of mischief that is wholly Alsop.

Instead of dull secondary cubicle-like rooms, there are three curvy pods set on more stilts, each clad in wafer-thin timber scales stitched together with copper wire. At one end, the pod is a beehive-like meeting room. In the centre is an open-platform, like a big coracle, acting as an Afro-Caribbean centre. The third pod, again enclosed, is for children. It contains a place to slap paint around (very Alsop), a little stage for performances or readings, mechanically-operated butterfly flaps to a skylight and, best of all, tiny tip-up timber shutters allowing children to peek at the adults on the main floor beneath, and no doubt occasionally flick pellets and giggle a lot. The two enclosed pods stick up through the flat roof like dinosaur eggs. As does the bright orange "tongue" - which turns out to be the sunshading cap for a Soanian circular lantern acting as a ventilator for the whole building, which eschews air-conditioning.