Hernán Cortés did not defeat an "Indian" civilization—a term properly referring to the peoples of the Indian subcontinent. In 1519–1521, he led the conquest of the Aztec Empire (the Triple Alliance of Tenochtitlan, Texcoco, and Tlacopan), a sophisticated Mesoamerican civilization centered in the Valley of Mexico.
The Aztecs (who called themselves Mexica) ruled a vast tributary empire with a capital, Tenochtitlan, that was among the world's largest cities. Cortés succeeded through a combination of superior weaponry (steel, guns, horses), devastating epidemics (smallpox), and—crucially—alliances with Indigenous peoples (notably the Tlaxcalans) who were enemies of the Aztecs. The fall of Tenochtitlan in 1521 marked the beginning of Spanish colonial rule in Mesoamerica.