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. 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?