The Milan Cathedral is the largest church in Italy and the third largest in the world - a forest of spires and statues, pink Candoglia marble, Gothic ambition that took nearly six centuries to complete. Construction began in 1386 under Gian Galeazzo Visconti; the facade was not finished until 1965, when the final bronze doors were installed. The delays were not poverty but perfectionism; each era revised the plans of the one before.

The rooftop is the revelation. Visitors climb stairs or take elevators to walk among the 135 spires and 3,400 statues, the Madonnina gold statue at the highest point watching over the city. The view extends to the Alps on clear days; the spires and flying buttresses, viewed from above, reveal the cathedral's scale as the interior cannot. Napoleon crowned himself King of Italy here in 1805, the ceremony meant to rival Charlemagne's coronation eight centuries earlier. The Duomo serves both worship and tourism, mass in the mornings, selfie sticks in the afternoons.

Leonardo da Vinci painted The Last Supper between 1495 and 1498 on the refectory wall of Santa Maria delle Grazie, using an experimental technique that began deteriorating almost immediately. The painting has been restored repeatedly, sometimes badly; what visitors see today is partly Leonardo, partly accumulated intervention, partly imagination filling gaps that damage has created. The work remains one of the most famous images in Western art, the moment of Christ announcing betrayal captured in the disciples' varied reactions.

Viewing requires advance booking, often weeks ahead; groups of 25 are admitted for 15 minutes each, the time strictly enforced, the climate carefully controlled. The experience is pilgrimage as much as tourism - the wait, the anticipation, the brief communion with genius. Napoleon used the refectory as a stable; Allied bombing in 1943 destroyed much of the church but left the wall standing. The painting survives because Milan has protected it obsessively, the decay that Leonardo's technique guaranteed only making preservation more urgent.

Milan Fashion Week draws buyers and press from around the world four times a year, presenting the collections of Italian houses - Prada, Armani, Versace, Dolce and Gabbana - alongside international labels that have established presences here. The Quadrilatero della Moda, the fashion district bounded by four streets near the Duomo, holds the flagship stores and showrooms where luxury is displayed and sold.

The fashion industry employs tens of thousands directly and shapes the city's economy and identity beyond the showrooms. The Salone del Mobile, the annual furniture fair, is fashion's equivalent for design. The brands that began in Milan or relocated here have made the city synonymous with Italian style - the sleek minimalism of Armani, the baroque excess of Versace, the intellectual rigor of Prada. The fashion capital emerged from the textile industry that once made Milan wealthy; the transformation from making cloth to making statements happened over decades, deliberately cultivated by designers who chose Milan over Paris.

Milan is Italy's financial capital - the Borsa Italiana stock exchange, the headquarters of major banks and insurance companies, the offices of multinationals that use Milan as their European base. The business culture is closer to Frankfurt than to Rome; the work ethic is stereotyped as northern European rather than Mediterranean. Milanese consider this a compliment.

The financial center developed because Milan had industry that needed financing, and industry developed because Milan had geography - the Lombard plain suitable for agriculture and manufacturing, the Alps providing hydroelectric power, the position at the intersection of European trade routes. The finance serves the fashion and the design and the manufacturing that make things; unlike London or New York, Milan's finance is not an end in itself. The city makes money by making products, then makes money from money, the layers building on a foundation that Rome has never replicated.

Milan's reputation is efficiency - the metro runs on time, the businesses operate professionally, the pace is faster than Italy expects. The stereotype has truth in it, though Milanese grumble about dysfunction like everyone else. The city rebuilt itself after wartime destruction with determination that other Italian cities lacked; the economic miracle of the 1950s and 1960s was concentrated here, in factories producing the Vespas and appliances that symbolized postwar prosperity.

The city continues to work, adapting to each era's demands. The Expo 2015 generated development that transformed former industrial areas; the three new skyscrapers of the Porta Nuova district announced that Milan could build vertically as well as horizontally. The city competes with European rather than Italian peers - with Munich and Barcelona and Amsterdam - while Rome remains provincial in ways Milan considers embarrassing. Whether this is admirable ambition or cold arrogance depends on whether you prefer your Italy efficient or romantic. Milan chooses efficiency.