The famous conqueror known for his expeditions to India and Mexico is Hernán Cortés. He was a Spanish conquistador who led the expedition that resulted in the fall of the Aztec Empire in 1521. His conquests were driven by a desire for wealth, glory, and the spread of Christianity. Cortés's interactions with indigenous people, including alliances with rival tribes, played a crucial role in his success. His later expeditions to other regions, including attempts to explore parts of the Pacific coast of North America, contributed to Spain's vast territorial claims in the Americas and the significant cultural exchanges between continents.