Hernan Cortes was a Spanish conquistador who came to the New World with intentions of forging a new empire for Spain. Famously, he showed up on the shores of Mexico with his small army of cannon, horse, and musketmen and put the entire Aztec Empire to the sword. Burning his ships, Cortes showed there was no way out except victory. Within three years, the capital of the Aztec Empire would be conquered, in:
The Fall of Tenochtitlan
Hernan Cortes had formed an alliance with the native city of Tlaxcallan, combining his technical superiority with the numbers Tlaxcallan could offer. This helped to alleviate the difficulty that Cortes had originally faced: the Aztecs outnumbered him something like 200:1. The two allies then set out to divide and conquer, knocking out as many of the Aztecs' allies as possible before laying siege to the Aztec capital of Tenochtitlan in May of 1521.
Cortes's plan was fairly simple. He sent his Spaniards to block off the three causeways that were the only route into Tenochtitlan, and to take out the water supplies by Tlacopan. The Aztecs used canoe-warriors to outflank the Spaniards and won the Battle of Tlacopan, stopping that advance. So Cortes opened up a causeway to allow his brigantines access to the lake, letting him dominate all the waterways around Tenochtitlan.
The Spaniards attacked the Aztec positions on the causeway during the day and fell back during night, but this led to very little motion in the end. However, Cortes was wearing the Aztecs down; dysentery and smallpox were ravaging Tenochtitlan, and no reinforcements were coming from the few Aztec tributary cities left, as they feared being left open to Spanish attack. However, the Spanish did receive more soldiers and ammunition from their port at Vera Cruz.
Eventually, with extra reinforcements, Cortes broke the Aztecs and entered Tenochtitlan. After the Spanish encountered a traditional "Aztec Owl-Warrior" and failed to kill him, the Aztecs took this as a sign that though defeated, they would live on. They surrendered.
Yeah. Right. Cortes killed the Aztec leader, Cuauhtémoc, and sacked Tenochtitlan. Something like 240,000 Aztecs died during the siege. And Cortes laid the foundation for New Spain, a colonial empire that would last until the 1800s and exploit the New World for pretty much everything it could.
Also, the conquest of the Aztecs set a dangerous precedent of "the savage" that would be popularized in Europe, leading to similar treatment of Native Americans for hundreds of years. While the various anti-native atrocities of the European settlement of the Americas likely still would have happened, Cortes was part of the first major extermination of a native group; and many more would follow.