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Do flying buttresses, art deco curves and Cor-ten make you weak at the knees? If architecture's your thing you'll appreciate just how much influence it has on a city's character. It reflects the ideology of a place at a particular point in history, demonstrates its pioneering spirit, and at times, becomes the symbol of the city – just think of the Eiffel Tower.

The architecture of Paris, New York and London often gets all the limelight, so here are a few alternatives and why you should visit them.

Barcelona for the colourful, sculptural creations of Antoni Gaudí

Over 2000 years of architectural history litter the streets of Barcelona where Roman ruins and Gothic cathedrals mix with the whimsical, undulating designs of Catalan modernist Antoni Gaudí. Renowned for his use of organic forms and flamboyant colours, his unfinished masterpiece, , is still taking shape 130 years after it was begun. This giant, dream-like basilica is a trippy tangle of organic shapes that breaks all architectural moulds. Wander about the city to see more of his creations such as Casa Batlló and Park Güell.

Top tip: See Gaudí's work in style by taking in a summer concert on the roof of La Pedrera.

Chicago for architectural innovation

The Great Chicago Fire in 1871 destroyed most of the city's downtown and paved the way for the construction of the world's first skyscraper, the 10-storey Home Insurance Building. Since then, Chicago has earned a reputation for architectural experimentation with arresting high-rise creations and the work of pioneering modernists, such as Frank Lloyd Wright, littering the city. Home to the for 25 years, the tradition of architectural innovation continues in the undulating, sculptural Aqua Tower and the geometric glass of the .

Top tip: Buy a drink on the 96th floor Signature Lounge of 360° Chicago and you'll get the view for free.

Istanbul for a collision of classical influences

Sitting astride two continents at the end of the Silk Road, Istanbul has been a hub of trade, power and culture for thousands of years. Its legacy is a staggering array of monuments, palaces and towers illustrating Greek, Roman, Byzantine and Ottoman influences. The extraordinary beauty of the 6th-century Aya Sofya with its colossal Byzantine dome and glittering mosaic work makes it the city's greatest landmark, a title hotly contested by the palatial, 17th-century Blue Mosque and the Topkapı Palace, once the heart of the Ottoman Empire.

Top tip: Head for a rooftop bar at sunset to see the city's magnificent skyline at its best.

Rome for classical elegance and ingenuity

Awash with ancient ruins and Renaissance churches, Rome is home to some of the most significant and influential buildings in the Western world. Wander around the Colosseum and Palatine Hill for a sense of ancient power and glory. Marvel at the ingenuity of the Pantheon, a 2000-year-old engineering masterpiece, strain your neck as you admire the work of Michelangelo and Bernini in St Peter's Basilica or just stroll the streets and happen upon countless Baroque palaces and flamboyant fountains.

Top tip: Avoid the Colosseum queues by buying your ticket at the Imperial Fora and using the automatic ticket barrier instead.

Mumbai for colonial-era grandeur

Mumbai's architecture is as eclectic and flamboyant as the city. Its temples, mosques and synagogues mix with glittering tower blocks, art deco cinemas and glorious Victorian-era monuments of colonial extravagance. It's these neo-Gothic and Indo-Saracenic structures that give Mumbai its architectural aplomb and most famous of all is Chhatrapati Shivaji Terminus, one of India's busiest train stations and an exuberant jumble of Victorian, Hindu and Islamic styles. More sedate is a stroll through Chhatrapati Shivaji Maharaj Vastu Sangrahalaya, Mumbai’s biggest museum, or afternoon tea at the Taj Mahal Palace.

Top tip: Stroll through the High Court where robed barristers add pomp to the grand Gothic-revival building.

Miami for art deco indulgence

Set against blue skies and swaying palms, the art deco mansions of sunny South Beach still ooze the elegance and glamour of the 1930s. The city's historic district has the largest collection of art deco buildings in the world, most built between 1923 and 1943 in an effort to attract wealthy northerners to the budding resort town. Stroll down Ocean Dr and Collins Ave to see some of the hundreds of low-rise, pastel-coloured hotels, shops and houses with their streamlined, symmetrical style, stepped roofs and curved corners.

Top tip: Visit in January for the when classic cars flood Ocean Dr.

Oxford for Gothic revival glory

Oxford's architecture is intrinsically linked with that of its university, its most famous landmark the Radcliffe Camera, an elegant, neo-classical rotunda used as a university reading room. It's part of the Bodleian Library which is also home to the Divinity Room with its glorious lierne vaulting and the Tower of the Five Orders, built according to the five classical orders of architecture. Of the colleges, Christ Church and Magdalen are the largest and grandest, while the stunning neo-classical Ashmolean Museum and the elegant Victorian Gothic , top the cultural bill.

Top tip: Get inside the hallowed Radcliffe Camera on the extended tour of the Bodleian Library.

Shanghai for art deco excess and sci-fi skyscrapers

Renowned for its futuristic skyline and constant frenzy of building work, Shanghai also offers 'Chinese deco' exuberance along and in the leafy French Concession. Take stock of it all from the world's highest observation deck on the twisting Shanghai Tower. Glittering tower blocks spread in every direction, the most obvious the neo-futurist Shanghai World Financial Centre. Back on the ground seek out the Himalayas Museum with its root-like exterior and the Oriental Art Centre with its interconnecting hemispherical petals.

Top tip: To sample Chinese deco in style have a drink in the Long Bar at the Waldorf Astoria.

µþ°ù²¹²õí±ô¾±²¹, a planned vision of the future

The brainchild of Brazilian architect Oscar Niemeyer, µþ°ù²¹²õí±ô¾±²¹ is a glorious experiment in late '50s modernism. Niemeyer's vision of the future centres on the arresting, crown-like Catedral Metropolitana. Its 16 parabolic concrete columns reach for the sky as you sit below ground surrounded by soaring stained-glass windows opening to the heavens. Nearby, the half-dome Museu Nacional wouldn't look out of place on a sci-fi film set, while the Three Powers Square emanates benign authority in the striking judicial, presidential and congressional buildings.

Top tip: See inside the Palacio da Avarado, the president's official residence and Niemeyer's most beautiful creation, on Wednesday afternoon tours.

Baku for ancient lanes and postmodern wonders

The capital of Azerbaijan, Baku is a dynamic, fast-developing city where Islamic, Soviet and postmodern architecture collide in a gloriously unpredictable melee. It's a chaotic but wildly energising blend of medieval laneways in the Old City and bold, brash designs on the waterfront. Survey the Old City from the Maiden's Tower before heading for the city's star attraction, Zaha Hadid's sinuous Heydar Ó˜liyev Cultural Centre which rises seamlessly from a large plaza into an elaborate series of shape-shifting folds.

Top tip: Wander down the waterfront at night to see the light show projected on the sinuous Flame Towers.

Read more on city tripping: The urban evolution: how city travel is changing.

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