The Spanish couldn&rsquot believe their eyes when they first arrived in Tenochtitlan in 1519. The capital of the Aztec, built in the waters of Lake Texcoco, was one of the largest cities in the world at the time, with 200,000 people living in it. Three causeways led to it across the water canals crisscrossed the city to allow transport by canoe four busy marketplaces supported thousands of traders. At the centre of the city was the pyramid of the main temple surrounded by public buildings and the palaces of the tlatoani or lord, Moctezuma II. One of the chroniclers of the Spanish conquest, Bernal D&iacuteaz, wrote, &ldquoI do not know how to describe this first glimpse of things never heard of, seen or dreamed of before&hellipI stood looking at it, and thought that no land like it would ever be discovered in the whole world.&rdquo

The Spanish, led by the conquistador Hern&aacuten Cort&eacutes, overwhelmed Tenochtitlan in less than two years. Eager to replace the religion and culture with their own, they systematically razed the city and rebuilt over it. The heart of Tenochtitlan, where its temples and palaces stood, turned into the seemingly European centre of Mexico City, the capital of New Spain.

Tenochtitlan does not exist today. But the assiduous tourist to Mexico City who also wants to travel back in time might just be able to piece it together.

A good place to begin is Xochimilco. The Valley of Mexico used to have five inter-connected lakes with Aztec settlements on islands and shores. These were filled in during colonial times as more land was required, and what remained more or less dried up as water tables fell. But the one corner that still retains the old system of canals is Xochimilco, a half-hour&rsquos drive south from Mexico City. The canals are now visited by groups of weekend picnickers from the city who take long, lazy rides in cheerily colourful barges constructed along the lines of pre-Hispanic vessels called acalli. Vendors and Mariachi bands drift alongside in canoes and boats. Also in the water (I am told) are axolotl, a critically endangered amphibian once eaten by the Aztecs and revered as an incarnation of their deity Xolotl. Now down to the last few hundred, these are found in the wild only in Lake Xochimilco.

Lining the canals are chinampas, which started out as large wooden rafts covered with soil for farming, but over time have piled up to form artificial islands. The city of Tenochtitlan grew much of its food on such chinampas. One of my self-effacing hosts tells me, &ldquoThese chinampas are probably the only thing completely unique to Mexico.&rdquo I hate myself even as I start telling him about Dal lake.

The original site of Tenochtitlan is now land-locked and coincident with what is now called the historical centre of Mexico City. This area is also the tourist centre with an endless supply of museums, churches, colonial buildings and, of course, the obligatory hotels, hostels, shopping and nightlife. The area is organised around the Zocalo, or city square, the second largest in the world after Moscow&rsquos Red Square. A Spencer Tunick photo-shoot in 2007 gives a sense of its size in human terms &mdash18,000 people lay sprawled here in the nude with room to spare. On one side of the square is the Palacio Nacional, from where Mexico has been ruled ever since people started living here. It was the site of Moctezuma&rsquos palace before Cort&eacutes had it felled and used much of the same stone to build his own palace. It became the official residence of the viceroy of New Spain, and after Mexico&rsquos independence in 1810 housed its two emperors and many of its presidents. The corridors of the Palacio Nacional are lined with Diego Rivera murals depicting pre-Hispanic life in Mexico. A large, dense mural on the main stairwell tells the entire history of Mexico after the colonial conquest.

At the Zocalo, the swirl of copal smoke and the sound of drums, rattles and anklets leads to a clearing where indigenous dancers in loin-cloths and plumed head-bands recreate ceremonial Aztec dances. Around here used to be the religious centre of Tenochtitlan. Even the snacks sold around here would not have been out of place then &mdash nopales cactus on crisp tortillas, boiled corn (but without the slathered mayo). Elsewhere on the streets one might find tamale, steamed corn cakes eaten in these parts for thousands of years. This is served with atole, a drink made from cornflour, sugar, water and spices.

The founders of Tenochtitlan were a wandering Mexica tribe waiting for the fulfilment of a prophecy they were to settle where they saw an eagle perched on a cactus. Historians argue about whether the prophecy included a snake in the eagle&rsquos beak, but the tribe saw something of the sort in 1325 on a small island in a swampy lake. The precise spot was commemorated by the main temple, the Templo Mayor. So thorough was the Spanish working-over that even the original location of the Templo Mayor was lost. In 1978, workmen laying electrical cables in the ground came upon a huge stone disc with a carving of the Aztec moon goddess. Archaeologists took over and excavated what turned out to be the remains of the Templo Mayor.

The Templo Mayor excavation is now open to the public. Visible are the bases of six nested pyramids, each of which was covered over by a succeeding ruler to build a larger one. Still discernible here are a living area for warriors, some painted stone carvings, a few stairs and courtyards. The excavation yielded relics now preserved in the adjoining museum sculptures of deities in stone and ceramic, knives of flint and obsidian, masks, beads, skulls, musical instruments, urns and beads.

Parts of the Templo Mayor show signs of being inspired by the much older city of Teotihuacan, forty-five kilometres to the northeast of Mexico City. The city was already abandoned by the time Tenochtitlan was founded, having seen its peak a millennium before. The Aztecs went there themselves as devout tourists, believing Teotihuacan to be where the gods sacrificed themselves to set the sun in motion. There is much that is uncertain about the history of Teotihuacan, but the enormous site of this planned city with its towering pyramids of the Sun and Moon, the Avenue of the Dead, and the Temple of the Feathered Serpent is one of the best-preserved examples of Mesoamerican grandeur and a haunting reminder of the transience of civilisations. (But such lofty abstractions are elusive while actually huffing up the pyramids. Humility and prayer pretty much suggest themselves about halfway up, and grow with each leaden step.)

The National Museum of Anthropology in Mexico City tells through charts, films, recreations and relics the story of humans in Mexico beginning with the first migration of people to the Americas. The Anahuacalli Museum, a pyramid-shaped structure built with volcanic rock, houses Diego Rivera&rsquos considerable collection of pre-Hispanic artefacts. These museums provide insights into life and culture in Mesoamerica, and in particular Tenochtitlan. Much has been made, for instance, of the Aztec practice of human sacrifice, but it is useful to see this in the larger context of a people for whom rites and sacrifices signified more than mere bloodlust. These were ways to propitiate the earth, sun and rain, all of which sustained people. They also linked human life (and death) with the workings of the universe, and made the individual significant. Hence the wars meant solely for capturing sacrificial candidates, the willing participation of individuals in rituals ending in their own death, and the pre-occupation with valour.

Why bother with Tenochtitlan now, almost five hundred years later Here&rsquos an oblique and hopefully not entirely fanciful answer.

A drinking game called toque is played in the bars and cantinas of Mexico. It is offered by men with contraptions round their neck consisting of a battery, wires and electrodes. The group sitting at a table links hands and completes the circuit through the electrodes. The toque-man sends increasing bursts of electric current through the group. Those alarmed by the tingling in their hands let go and the rest form a closer circle until there is only one left, the winner. Many virtues are vaguely attributed to toque it enhances virility, gets you sober, prevents a hangover, purifies blood, and so on. It&rsquos harmless and fun, but to see two drunk men battle it out to the end is to witness a sloppy gladiatorial contest alchemise into something transcendent. It&rsquos not just about winning, it&rsquos somehow about everyone and everything. Toque is a modern game designed in Tenochtitlan.

There&rsquos a cultural sensibility that seems to have originated in Tenochtitlan too. Mexican culture engages with death more often, and more irreverently, than any other. The Day of the Dead is an important festival in Mexico, when elaborate altars are made with offerings to the dead, and calaveras &mdash skulls &mdash are made from sugar and chocolate to be eaten. The festival has been celebrated since Aztec times, though it has since acquired a Catholic veneer. In the early twentieth century a print-maker named José Guadalupe Posada caricatured prominent personalities as skeletons. Thus began the uniquely Mexican tradition of representing the activities of the living using skeletons. The Museum of Popular Art in Mexico City has a large number of these on display (though it is best known for its annual parade of fantastical creatures starting from the historical centre).

The Spanish infused into Mexico their religion, language, and, by marrying indigenous people, their blood. After independence, Mexico embarked on its modern identity by rooting itself in Tenochtitlan. It took the image of the cactus, eagle and snake for its flag. And like the Templo Mayor emerging from the ground, aspects of pre-Hispanic culture continue to resurface. It is common to see people queued up at the Zocalo to be cleansed by copal smoke. The traditional steam bath, the temazcal, has grown in popularity in recent times. The food and drink continue to be a synthesis of pre-Hispanic and Spanish influences.

A place in Mexico City that symbolises the evolution of Mexican identity is the Square of the Three Cultures in Tlatelolco, once the sister city of Tenochtitlan. The square has Aztec temples, a Spanish church and offices and a housing complex that invoke the mixed population of the present day. More ominously, it was here that at least three hundred unarmed student protesters were killed by government forces in 1968. The writer Octavio Paz &mdash who resigned as Mexican ambassador to India in anger at the massacre &mdash proposed another connection between the three cultures. He suggested there was a totalitarian streak in the Mexican regime of the time that was linked through the Spanish viceroys to the spirit of the Aztec tlatoani.

A walk through the stately solidity of central Mexico City can give one the impression of being in a nameless European city. The difference lies in the distant rumble of history and its expression in the culture that is around. The material for colonial construction and even the paving stones underfoot came from the rubble of the Aztec city, and it still shimmers in the gaps between the churches and baroque buildings.