In 1325, somewhere in the shallows of Lake Texcoco in central Mexico, a group of wanderers stopped walking. They had been searching for a sign: an eagle perched on a cactus, devouring a serpent. When they found it on a small, swampy island, they did not hesitate. They drove stakes into the mud and began to build. That city, Tenochtitlan, would grow within two centuries into the capital of the most powerful empire in the Americas. The people who built it called themselves the Mexica. The world would come to call them the Aztecs.

The Mexica were latecomers. Nahua-speaking peoples had been filtering south into central Mexico from the arid north since the early thirteenth century, and by the time the Mexica arrived around 1250, the best farmland was already claimed. They were given a scrubby, infertile patch near Chapultepec by the king of the small but prestigious city-state of Culhuacan, and they served that city as mercenaries. They were outsiders, landless and subordinate, fighting other people's wars to survive.

Their subordination did not last. The Mexica were ferocious soldiers, and warfare was not merely practical for them: it was sacred. Their patron god, Huitzilopochtli, the war deity of the Mexica, demanded the hearts of captured enemies to keep the sun moving across the sky. Capturing a live prisoner in battle was the single greatest act of honour a Mexica warrior could perform. This theology of conquest gave the empire both its energy and its brutality.

After a violent falling-out with Culhuacan, involving the ritual sacrifice of a king's daughter, the Mexica were expelled and retreated to their island. They found their sign. They founded their city. And they allied themselves with the dominant regional power: the Tepanec city-state of Azcapotzalco, whose ruler Tezozomoc was building his own small empire in the Valley of Mexico. Under Tezozomoc, the Mexica fought, and fought well, and were rewarded. Their first recognised king, Acamapichtli, was enthroned in 1372.

The arrangement with the Tepanecs held until 1426, when Tezozomoc died and his son Maxtla seized power in a coup. Maxtla turned on his father's allies. The Mexica ruler Chimalpopoca died under suspicious circumstances, almost certainly killed on Maxtla's orders. The new Mexica ruler Itzcoatl refused to submit. Maxtla blockaded Tenochtitlan and demanded heavier tribute. Meanwhile the king of Texcoco, a brilliant administrator named Nezahualcoyotl, had been driven into exile by the same coup. He began raising an army.

In 1427, Tenochtitlan, Texcoco, and a dissident Tepanec city called Tlacopan went to war against Azcapotzalco. By 1428, the Tepanec empire was broken. Maxtla was defeated, and the three victorious cities signed a treaty dividing the spoils. That agreement, known as the Triple Alliance, became the constitutional foundation of what the world calls the Aztec Empire. Tribute collected from conquered lands was split between the three cities, with Tenochtitlan and Texcoco each taking two shares and Tlacopan one. The three rulers assumed the joint title of huetlatoani, meaning Elder Speaker, or Emperor.

From the start, the empire was shaped by two men close to Itzcoatl: his nephews Tlacaelel and Moctezuma. Tlacaelel took the newly created role of Cihuacoatl, something between prime minister and viceroy, and he used it to remake Mexica identity from the ground up. He reportedly ordered the burning of existing historical records, claiming they contained lies, and rewrote the Mexica's past to place them at the centre of divine history. Moctezuma, meanwhile, proved a brilliant general and eventually succeeded Itzcoatl as emperor in 1440.

Under Moctezuma the First, the empire's machinery was refined. Conquered cities were allowed to keep their own rulers, provided those rulers paid semi-annual tribute and supplied soldiers when called upon. Those who refused were replaced with puppet governors. Nezahualcoyotl introduced a clever incentive in his own Texcocan lands: cooperative kings received tribute from distant territories, but if they rebelled, they lost those distant revenues instantly. The empire did not rule by garrison; it ruled by economic dependency.

New laws reshaped society at home. Moctezuma the First separated nobles from commoners by statute and created a new title, quauhpilli, a form of non-hereditary lesser nobility that could be awarded to commoners for exceptional military or civil service, something like a knighthood. Religiously supervised schools were built in every neighbourhood: the telpochcalli for commoners, providing basic military and religious training, and the more prestigious calmecac for the nobility and those commoners destined for the priesthood.

One of the most distinctive institutions of the empire emerged from a catastrophe. Between 1450 and 1454, a devastating drought gripped the Valley of Mexico. Tlacaelel's response was theological: the gods needed more prisoners. From this crisis came the Flower Wars, a formalised system of ritual combat pre-arranged between the Aztec Empire and its neighbours, especially the rival city-states of Tlaxcala, fought not to conquer territory but to generate a steady supply of prisoners for sacrifice. Both sides agreed to the terms. Both sides sent their best warriors. The battles were real and the casualties genuine, but the purpose was sacred.

Expansion continued regardless. Itzcoatl and Nezahualcoyotl had already pushed beyond the Valley of Mexico into the region of Morelos. A four-year drought briefly halted this momentum in 1450, and several conquered cities had to be re-taken when order collapsed during the famine. After Moctezuma the First died in 1468, his son Axayacatl spent most of his thirteen-year reign consolidating territories already won rather than pushing new frontiers. The empire was vast but restless; provinces rebelled constantly, and each rebellion required a military response.