It's nearly impossible for first-time visitors to appreciate just how fast Dublin is moving. Native "Dubs," however, who left years ago and returned to the "Celtic Tiger" economy, can't believe their eyes. Their beloved -- if slightly down-at-the-heels -- hometown has metamorphosed into a bastion of trendy coffee shops and juice bars, fusion-cuisine restaurants, minimalist interiors, designer boutiques, and Mercedes-Benz and BMW dealerships. Ireland is the fastest growing economy in the European Union and is now entering its seventh consecutive year of economic growth -- averaging 9% a year. And Dublin, as its capital, is at the epicenter of the boom.

What's amazing is not that Dublin has gotten so hot, but that it's happened so quickly. In 2000, Fortune magazine named Dublin among the top 5 European cities in which to do business -- an accolade fueled, no doubt, by its reputation as the "Silicon Valley" of Europe and strategic Euro-headquarters for such computer giants as Microsoft, Dell, Intel, and Sun Microsystems. Also in 2000, an annual survey of world cities conducted by William M. Mercer Ltd. ranked Dublin among the world's top-10 most livable cities -- above New York, Boston, and Washington, D.C. The word has gotten out: For work or play, Dublin is the place to be.

Twenty years ago most visitors to Ireland either bypassed "dirty ol' Dublin" altogether or made a mad dash from the ferry to the train station, determined to spend their first night beyond the pale. Now the opposite is the case. Dublin certainly gets the glamour vote as one of Europe's trendiest cities. Sightings of Gwyneth Paltrow, Julia Roberts, Robert DeNiro, and Cate Blanchett have become so commonplace that locals barely blink an eye. (The Irish polite indifference to celebrity is a slice of nirvana for privacy-loving stars.)

Greater Dublin's population has swollen to 1.5 million; in other words, more than a third of the entire country lives here. The time has passed when aspiring Irish artists owed it to themselves to emigrate. Today, they dig in. If Joyce and Beckett and Wilde could see Dublin today, they'd be back. Dublin is simply contagious, and its addictive quality isn't in the Guinness. It's where it's always been, in the people.

Dublin, like most ancient cities, lies sprawled along a river. The Liffey has divided Dublin into north and south for more than 1,000 years. Neither as romantic as the Seine nor as mighty as the Mississippi, the Liffey is just there, old and polluted, with walls to sit on or lean against when your legs give out. Still, it is and always has been the center of things here, and it does make for a pretty picture on a good day. Despite all the changes, the Liffey continues to divide the town as it once divided Viking from Celt and Norman from Norse.

So far, the buzzing, prosperous hub of Dublin lies mostly south of the Liffey. The area containing most of the best hotels, restaurants, shops, and sights is a small, well-defined compound that can be easily walked in a half-hour. It comprises a large part of Dublin 2 (the postal code for each neighborhood is listed in "The Neighborhoods in Brief," below), beginning with the Georgian elegance of St. Stephen's Green, moving toward the river via bustling Grafton Street, heading farther north and west through the trendy cafe scene of Temple Bar, and even farther west to the capital's hippest new shopping district, known as "Old City."

That said, a visit confined to this small pocket of Dublin is not a true visit to Dublin. An hour's walk from the top of Grafton Street, across the Liffey, up O'Connell Street, and farther into north Dublin is a walk through time and, simultaneously, a glimpse of some of the pieces that must eventually fit together. Explore, get a haircut (in a barbershop, not a salon), get lost and ask directions, and you may uncover a time capsule from the Dublin of a century ago -- or was it only a generation?