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Like any big city, however, residents cope by breaking it down into neighbourhoods on a more human scale. Here in these delegaciones (boroughs) you will discover a city that is one of the world’s most exciting.
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The historic centre is the obvious stop for first-time visitor. Here the Plaza de la Constitución is one of the world’s largest public squares, so huge that it dwarves the football-pitch-sized Mexico flag flying over it.
A former unfinished 19th-century monument that stood here gives the square its popular nickname of El Zócalo (“The Plinth”).
The buildings around include the Palacio Nacional (Presidential Palace), which is built of stone from Aztec emperor Montezuma’s palace. There are also luxury hotels, shops and various government offices but the main attraction is the Catedral Metropolitana.
Started in 1571 and finished in 1788, the cathedral was also built with Aztec stone and is among the oldest and largest in Latin America.
You can see a dramatic tilt in the building, which is sinking under its own weight into the dried lakebed on which the city stands. Inside, its 14 chapels fight with each other in the wealth of gold, paintings and statuary.
Most are in Mexico’s ornate churrigueresque style, named for 18th-century architect José Churriguera.
This was also the heart of the Aztec city and the front of the cathedral is a popular place for “Aztec dancers” to gather.
More authentic Aztec history can be found at the Templo Mayor nearby where archaeologists are still uncovering treasures, some of which are on display in a museum onsite.
The Zócalo is also a place for political protest and an understanding of Mexico’s complex history can be had by seeing Diego Rivera’s “Epic of the Mexican People” mural at the Palacio Nacional. More of the artist’s work is at Palacio de Bellas Artes, which houses two museums and sits next to the lovely and lively Alameda Park.
The park takes its name from its long-gone cottonwood trees (“alamos”) and holds another Diego Rivera mural, “Dream of a Sunday Afternoon in the Alameda”, in a specially built museum.
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Coyoacán (“Place of Coyotes”) was a small town of its own until swallowed up by the expanding city but it still has an independent, bohemian feel.
Its cobbled streets and colonial houses are the places to find artisan coffee shops, craft markets and edgy new restaurants. If you’re excited by modern Mexican cuisine, and you should be, this is a good place to try it.
However, this arty neighbourhood was more famously home to monobrowed artist Frida Kahlo, husband Diego Rivera and her lover Leon Trotsky.
The Frida Kahlo museum, also known as La Casa Azul (The Blue House) for its brightly painted walls, is the place of her birth as well as the home and studio she shared with Rivera.
She died here in 1954 and it remains a site of pilgrimage for her fans, preserved as it was during her lifetime. Her bed, with a mirror above it that allowed her to see the outside world, is especially poignant.
Museo Casa de Leon Trotsky is where the revolutionary lived with his wife for two years after being exiled from the USSR in 1936. Preserved as it was when he was alive, it is also where he was murdered with an ice pick in 1940. He had survived an earlier assassination attempt when a gang of 20 men fired at the house with machine-guns.
Diego Rivera has his own art museum in Coyoacán, Museo Diego Rivera Anahuacalli, but this mainly holds his collection of 60,000 pre-Hispanic work.
Rivera designed the building himself, in the form of a pyramid of black volcanic stone, and one floor is dedicated to his life and his work.
Diego built a joint home nearby with his wife: two Modernist three-storey houses linked by a roof bridge. Now preserved as Museo Casa Estudio Diego Rivera y Frida Kahlo, his home looks as if the artist could walk back in the door at any time.
Other places in Coyoacán to immerse yourself in Mexican culture include Museo Nacional de Culturas Populares; Centro Nacional de las Artes; Cineteca Nacional (National Film Archives); and Museo Nacional de las Intervenciones.
The strange name of this last hides the fact that it is both a well-preserved former colonial monastery as well as museum dedicated to a military history of Mexico, much of which involved “interventions” by foreign aggressors such as Spain, France and the US.
The continuing influence of Catholicism on Mexico can also be experienced at the striking Baroque church and former convent of San Juan Bautista. Built over a school for the children of Aztec nobility, it is one of the most beautiful churches in Mexico City.
Another formerly independent city, Xochimilco is best known for its canals, which are the last remnant of a lake on whose dry bed Mexico City now stands.
The Aztecs started a process of sinking juniper branch rafts planted with vegetables that eventually turned into small islands. Brightly painted “trajineras” boats that were once used for shipping goods around this market garden area are now filled with visitors.
The cool shady waterways make for a welcome escape from the heat of the city in summer or at weekends.
As you cruise on a few of the 100 miles of canals, other boats will come alongside to sell you crafts, T-shirts or food, or bring a Mariachi band keen to sing you a song for a few dollars.
The area has been recognised as a World Heritage Site by Unesco and the wetlands are also an important waterbird refuge.
Water loss, pollution, invasive species and other problems such as illegal settlements are a major concern for its future but Xochimilco remains a colourful must-see. An eco park on one of the islands is unexpected sight in Mexico City but is trying to educate school children about preserving the environment.
From music to religion - find out more about the cultures and traditions of Mexico
This upmarket area is the place to find the city’s elite shopping for luxury labels, enjoying fine dining or emerging from five-star hotels. Avenida Presidente Masaryk is the city’s equivalent of New York’s Fifth Avenue and Pujol ranks among the world’s top restaurants.
It’s the place to spend a lot of money or just have any negative preconceptions about Mexico City dispelled as you enjoy street life and people watching.
With more than 150 museums, Mexico City ranks only second to Paris as the city with the greatest number and this area is also home to several excellent ones.
The Museo Nacional de Antropología (MNA) is among the world’s finest, showcasing Mexico’s pre-Columbian heritage with treasures such as the “Stone of the Sun”.
Also known as the “Aztec Calendar Stone” (its exact purpose is unknown), it was carved in 1479, 40 years before the Spanish arrived and was found deep under the Metropolitan Cathedral in 1790.
Archaeologists now believe it may have been a ritual altar for human sacrifices.
Other gems include dramatic major works of the Oaxaca, Olmec and Mayan civilisations but among the most memorable are also some of the smallest.
Gold tributes thrown as sacrifices into a sacred pond at Chichén Itzá in Yucatan give a taste of the countless treasures melted down by the Spanish conquerors and now lost to the world forever.
Chapultepec Park is a pleasant oasis in the city and holds the educational Museo Nacional de Historia (MNH) inside Chapultepec Castle, once home to Emperor Maximilian I and with the appropriate marble staircases and gilded walls.
Other museums in the area include the Museo Rufino Tamayo, one for those interested in contemporary art, and Museo de Arte Moderno, which has works by the likes of Remedios Varo and, of course, Frida Kahlo and Diego Rivera.
Find out more about the history of the Maya and how it shaped the Mexico of today
The origins of Teotihuacan (“Birthplace of the Gods”) are a mystery, having been built and subsequently abandoned more than 1,000 years before the arrival of the Aztecs.
It was among the world’s largest cities at its height between 150 BCE and 750, with an estimated population of 125,000, but was abandoned for unknown reasons. The site 30 miles north of the capital now sees more than a million visitors every year.
The heart of the city is the 2.5-mile-long long “Avenue of the Dead” with a pyramid at each end. Work probably began on the Pyramid of the Sun in the first century, some 200 years after the origins of Teotihuacan itself, and the completed structure is the third-largest pyramid in the world.
The Pyramid of the Moon is a series of six structures all built atop each other until about 350 AD. A burial vault inside, found only in 2004, contained the ancient remains of 12 people, ten of them decapitated and with their hands bound behind their backs.
A good guide is essential to explore what is a vast complex, steeped in history, whose secrets are still being unlocked.
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