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Are they mono- or poly- theistic? What/is their god/s?

The Incas were polytheistic meaning they worshipped more than one God. The Incas believed there were many Gods as aspects of the world. For example they have a god of the Sun, Moon, Thunder, Earth.

Description of each:

Viracocha - Creator
Foremost of the celestial Gods, Viracocha was also worshipped by pre-Inca peoples living at Tiwanaku, near Lake Titicaca. Creator of the earth and its living creatures, Viracocha had formal titles such as Ilya-Tiqsi Wiraqocha Pacayaciq, "Ancient Foundation, Lord, Instructor of the World" or Wiraqocha Pachayachachi, "Creator of All Things". Although Viracocha was not as publically revered as Inti, the Sun God, Inca creation myths clearly place him as the most powerful.


Apu Inti - the Sun God
The royal rulers of the Incas claimed direct lineage Viracocha through Inti, the Sun, as he sired the first king. Inti was a male god, represented by icons as a golden disk or seated boy (Punchao) with rays projected from his head. The statue of Punchao bridged the gap between the supernatural and everyday world, as the vital organs of deceased rulers were burned and placed in his stomach. Golden images of his wives Inca Ocllo and Palpa Ocllo were kept with him in his temple.
Inti was the patron of the empire and conquest, and the Inca dedicated many ceremonies and rituals to him. The most powerful priest was the High Priest of the Sun, usually one of the ruler's close relatives or even the ruler himself, who led the innumerable ceremonies and festivals dedicated to the Sun God. Every major settlement in the empire had a Sun Temple, and crops and resources were set aside for the Sun's temples and activities throughout the provinces.


Chiqui Illapa - Thunder God
Also called Inti Illapa, the god of thunder and lightning was seen as a man in the sky wielding a great war club in one hand and a sling in the other. Lightning in the sky was said to be the sling stones he cast, and the Milky Way, called the Celestial River by the Incas, was the source from which he drew the rains. Because of his meteorological powers, Chiqui Illapa was the deity to which people addressed their prayers for rain.


Mama Quilla - Mother Moon
Mama Quilla was the wife of Inti, and in some coastal societies the moon was more important than the sun. Many rituals were based on the lunar calendar, and she had her own temple in Cuzco with attendant priestesses. Inca legend says the spots on the moon are from a fox who fell in love with her, and when he rose up into the sky to steal her she squeezed him against her and produced the dark patches visible today.

Pachamama - Earth Mother
Worshipped by farmers, the Earth Mother (also known as Mama Pacha) was a goddess who received many sacrifices of llamas and other animals to ensure successful harvests. Presiding over planting, harvesting and fertility, she is also sometimes depicted as a great dragon who causes earthquakes, and is still revered by some Andeans today.

Other Inca deities
Other important deities included Yakumama, the Mother Water; Mamacocha, the Mother Sea; and Pachacamac, Maker of the Earth and consort of Pachamama.

http://trailingincas.info/celestial.php

How does religion affect the hierarchy of their society? Do chiefs/priests have special religious importance?

Well, the chief was believed to be a descendant from Viracocha through Inti, the Sun. The chiefs were treated and seen as gods or as close as a human can get. In battle, the chiefs were like a beacon of divine power, giving warriors strength and a sense of protection. The priests of the Inca people were like ministers and had special healing powers to cure any disease. The priests were also the ones to perform sacrifices when the Incas won a battle or a great natural phenomenon happened.

How does religion differ from Western faiths?

Well, in Inca religion it is customary to perform human sacrifices to the gods after winning a battle or some natural phenomenon occurs. In fact, that was one reason the Spaniards killed so many of them when they "discovered" them, because they didn't belieave in the Spaniards one "God".