Which Native American groups did the Europeans encounter in South America?

Many indigenous groups existed in South American when the Europeans first arrived. 

The Spanish conquest of the Inca Empire, described in some detail by Diamond, began in 1532 when a small group of Spaniards led by Francisco Pizarro won Battle of Cajamarca. Part of the reason for this success was that the Inca were engaged in a civil war at the time. After a long period of fighting, the Spaniards finally subdued the Inca Empire in 1572, and established a colonial region encompassing much of modern Peru. 

Another major indigenous empire encountered by the Spaniards was the Aztec Empire, which occupied the central area of what is now Mexico. The Spanish leader Hernán Cortés and many native allies who supported him began the assault on the Aztecs in 1519 and were victorious in 1521.

The Mayan kingdoms of the Yucatán Peninsula of southeastern Mexico were conquered more gradually over the sixteenth and seventeenth centuries.