Most people visit Vienna with a vivid image of the city in their minds: a monumental vision of Habsburg palaces, trotting white horses, old ladies in fur coats and mountains of fat cream cakes. And they're unlikely to be disappointed, for the city positively feeds off imperial nostalgia - High Baroque churches and aristocratic mansions pepper the Innere Stadt, monumental projects from the late nineteenth century line the Ringstrasse, and postcards of the Emperor Franz-Josef and his beautiful wife Elisabeth still sell by the sackful. Just as compelling as the old Habsburg stand-bys are the wonderful Jugendstil and early Modernist buildings, products of the era of Freud, Klimt, Schiele, Mahler and Schönberg, when the city's famous coffeehouses were filled with intellectuals from every corner of the empire. Without doubt, this was Vienna's golden age, after which all has been decline: with the end of the empire in 1918, the city was reduced from a metropolis of over two million, capital of a vast empire of fifty million, to one of barely more than 1.5 million and federal capital of a small country of just eight million souls.

Of all Italy's historic cities, it's perhaps Rome which exerts the most compelling fascination. There's more to see here than in any other city in the world, with the relics of over two thousand years of inhabitation packed into its sprawling urban area. You could spend a month here and still only scratch the surface. As a historic place, it is special enough; as a contemporary European capital, it is utterly unique.

Since early in the nineteenth century Florence has been celebrated as the most beautiful city in Italy. Stendhal staggered around its streets in a perpetual stupor of delight; the Brownings sighed over its idyllic charms; and E.M. Forster's Room with a View portrayed it as the great southern antidote to the sterility of Anglo-Saxon life. For most people Florence comes close to living up to the myth only in its first, resounding impressions. The pinnacle of Brunelleschi's stupendous cathedral dome dominates the cityscape, and the close-up view is even more breathtaking, with the multicoloured Duomo rising behind the marble-clad Baptistry . Wander from there down towards the River Arno and the attraction still holds: beyond the broad Piazza della Signoria, site of the towering Palazzo Vecchio , the river is spanned by the medieval shop-lined Ponte Vecchio , with the gorgeous church of San Miniato al Monte glistening on the hill behind it.

Nobody arrives in Venice and sees the city for the first time. Depicted and described so often that its image has become part of the European collective consciousness, Venice can initially create the slightly anticlimactic feeling that everything looks exactly as it should. The water-lapped palaces along the Canal Grande are just as the brochure photographs made them out to be, Piazza San Marco does indeed look as perfect as a film set, and the panorama across the water from the Palazzo Ducale is precisely as Canaletto painted it. The sense of familiarity soon fades, however, as details of the scene begin to catch the attention - an ancient carving high on a wall, a boat being manoeuvred round an impossible corner, a tiny shop in a dilapidated building, a waterlogged basement. And the longer one looks, the stranger and more intriguing Venice becomes.

"Seville," wrote Byron, "is a pleasant city, famous for oranges and women." And for its heat, he might perhaps have added, since Seville's summers are intense and start early, in May. But the spirit, for all its nineteenth-century chauvinism, is about right. Sevilla has three important monuments and an illustrious history, but what it's essentially famous for is its own living self - the greatest city of the Spanish south, of Carmen, Don Juan and Figaro, and the archetype of Andalucian promise. This reputation for gaiety and brilliance, for theatricality and intensity of life, does seem deserved. It's expressed on a phenomenally grand scale at the city's two great festivals - Semana Santa (in the week before Easter) and the Feria de Abril (which starts two weeks after Easter Sunday and lasts a week). Either is worth considerable effort to get to. Sevilla is also Spain's second most important centre for bullfighting , after Madrid.

Barcelona has boomed since the early 1990s, when preparations for the Olympic Games wrenched it into modernity, and today it remains well in the vanguard of other Spanish cities (with the possible exception of Madrid) in terms of prosperity, stability and cultural activity. It's a confident, progressive city, looking towards the rest of Europe for its inspiration and its innovations - the classic tourist images of Spain seem firmly out of place in Barcelona 's bustling central boulevards and stylish modern streets. And style is what brings many visitors here, attracted by enthusiastic newspaper and magazine articles which make much of the outrageous architecture, user-friendly city design, agreeable climate and frenetic nightlife. Even the medieval Gothic quarter and its once-notorious red-light area have been swept up by the citywide renovation programme, which is still running at full tilt. As the new millennium starts Barcelona has continued to blossom from provincial city to putative European capital.

Madrid became Spain's capital simply through its geographical position at the centre of Iberia. When Felipe II moved the seat of government here in 1561 his aim was to create a symbol of the unification and centralization of the country, and a capital from which he could receive the fastest post and communications from each corner of the nation.