That blinkered view was of course no truer than previous predictions that video players and multi-channel TV would destroy everything from cinemas to football crowds. What happened instead was that the library tweaked itself a bit, offered a bit more, and got rather popular as a consequence. And then people discovered something else: a public library was not just a place to encounter various media including books. It was - and this was music to the ears of city planners - a catalyst for regeneration.

So suddenly libraries were cool again. They were no longer musty mausolea presided over by fearsome tweedy great aunts and inhabited by tramps keeping warm in the reference section. They were cultural venues. Since lots of people go to those, and since such crowds of people tend also to buy stuff, the same economic formula could be applied to a library as to a theatre or concert hall. And this is why a complete new square has been built in Brighton: the presence of a new library has made it happen.

Brighton has played its cards well. It has got itself a sophisticated new central library, cross-subsidised by other buildings around the square including housing, shops and a hotel, all wrapped up in one of those Private Finance packages that sees the building maintained for the next 25 years. They have also struck a 25-year deal with a book supplier. It's massively better than what they had before, it has rescued a derelict patch of land and connected up previously separated city districts. The library has become a superhero. The city did not save it: it saved the city.

This shift in attitude has been gaining momentum for a while. We've had Will Alsop's Stirling Prize-winning Peckham Library of 2000, we've had BDP's award-winning Bournemouth library of 2002 - the first to happen under the PFI banner - we have the expanding programme of archly-named "Idea Stores" in London's Tower Hamlets, two of which have been designed by the devastatingly fashionable architect David Adjaye. Not everything is going so smoothly - plans by Richard Rogers for a brand new £130m Birmingham city library have hit political and economic turbulence, for instance - but on the whole, the lending library is in rude health.

"Idea Store" is the sort of name they like so much in Tower Hamlets that the council has actually registered it as a trade mark. Elsewhere you come across the offputting phrase "learning centre". But in Brighton as in Peckham they see no reason to indulge in modish euphemisms. In fact the city's new pride rejoices in the thoroughly old-fashioned name of "Jubilee Library", named after a reinstated street that runs along one side of the scheme. In fact they've named the entire new square Jubilee Square. They just like the name.

The library is by architects Bennetts Associates, responsible for London's new Hampstead Theatre, and the local firm of Lomax Cassidy Edwards. It's a true collaboration: Rab Bennetts and Nick Lomax are old chums. They and Brighton's "major projects" team, headed by Katharine Pearce, have managed to pull the white rabbit of a good public building out of the black top hat of the private-funding process. Learning the trick was hard.

At a time when every other building in the western world seems to have an off-the-peg terracotta skin, Bennetts and Lomax managed to find a local ceramicist to make lovely hand-glazed tiles - metallic blueish in finish, each one slightly different - inspired by the 18th century "mathematical tiles", pretending to be bricks, that are a feature of Brighton. At a time when most buildings have standardised floors and ceilings, here they have made a lofty, noble interior which looks to have been inspired by Frank Lloyd Wright. A double-deck freestanding arrangement of floors and roof supported by tall columns and cruciform capitals - all moulded from concrete on site - defines the heart of the library. The lending library is on the ground floor - which is double-height - and the reference deck is above that. This dramatic arrangement stands inside a U-shaped sequence of back-up rooms, clad in pale beech: the two parts of the building are connected by access bridges and a broad glass strip at roof level.

It is a very low-energy building - shouldn't they all be, these days? What matters is the quality of the space you are sitting in, and Brighton has got itself a lot of high-grade space for those who will come for its books, its papers, its internet surf centre, its dvds and computer games, its bookshop and its café. Can't say I liked its shelving much - in fact it's awful. David Adjaye's serpentine plywood shelves in Whitechapel's far smaller Chrisp Street Idea Store are much more imaginative in the way they make enclosures without walls. But whereas Adjaye's building is a cramped, noisy souk of a place, Brighton's Jubilee Library, shelving aside, aspires to something else: the public lending library as a lofty expression of civilised values as much as a place to borrow words and images.

The library cost £14m: the new square will come in at around £60m once the hotel is built and the housing and shops finished. It aims to extend Brighton's "cultural district" by being set just north of the onion-domed Royal Pavilion, the Dome arts complex, city museum and art gallery and the Theatre Royal. By doing this, it connects the boho quarter of North Laine, getting up towards the station, with the much more touristy "Lanes" area of shops and restaurants further south. So this is joined-up thinking, an urban repair job. It is already stimulating more beneficial development around it.

For the moment, the Jubilee Library stands alone on its square. Builders continued to crash and screech around after it opened on world Book Day, March 3. The eventual quality of Jubilee Square will depend much on the hotel opposite, and on the success of the shops and restaurants alongside. But Brighton, for all that its one-time West Pier is now a tangled heap of twisted burnt-out metal in the sea, has a confidence about itself these days. Only officially a city since 1997, it is starting to behave like one. The revival of the old idea of the library is also the revival of public space and civic pride. It's hard to find a downside in that.