The similarity between the Aztecs, Mayans and Incas is that all had control of massive empires that eventually ceased to exist. Other than that common factor, the groups all had different ways of life and unique languages, political agendas, religious views and ways to provide for their people.
The Aztecs built an empire that was based in the area that is now known as Mexico City. At the time, the area that they controlled was known as Tenochtitlan. Their reign in this area occurred between the 12th and 15th centuries, until Hernado Cortes led the Spanish into the area and took over he city of Tenochtitlan with the help of other Indian tribes that were enemies of the Aztecs. The Sun and Moon pyramids of Tenochtitlan are still popular tourist attractions today.
Aztecs had a complicated and involved system of religion that focused on three main gods and several minor gods. Human sacrifice was often performed in the name of a god known as Huitzilopochtli. To capture prisoners to be used in human sacrifices, warriors would fight wars called "flower wars" with their enemies. It was during these wars that warriors were trained for battle by practicing their skills hands-on. Aztec designed and built the chinapas system of farming, which allowed them to grow crops in the swampy regions in which they lived. They spoke Nahuatl, a language very different from that of the Mayans and Incas.
The Incas built their empire hundreds of miles away from the Aztecs, starting in 1100 A.D. along the Pacific Coast of South America between Columbia and Chile. Their base of operations was focused in what is now Peru. Incas relied on peaceful negotiations rather than war to get their enemies to side with them, but their empire eventually was brought down during a civil war between two ruling princes that broke out when Spanish conquistador Francisco Pizarro arrived with a group of 180 soldiers. Pizarro took advantage of a smallpox outbreak that weakened the Inca population to capture the Inca king and replace him.
There was no human sacrifice in the Inca culture, like there was with the Aztecs. The Inca people were more peaceful and relied on diplomacy, but could be vicious fighters when pressed. The Incas designed and built thousands of miles of roads throughout their territories to make communication easier to manage. To feed their people, the Incas developed a system to be able to grow crops on the sides of the mountain in the Andes. They were one of the first cultures on record to heavily rely on the use of corn and potatoes for food. They used llamas for hauling and operating farm equipment. The Incas spoke a language known as "Quechua" and their educational system was only for nobility.
The Mayans were most active from 300 to 900 A.D. in urban developments that were built in the lowlands in the central region of southern Guatemala and extended south to Honduras. They were the one of the first people to create an urban centre in the midst of a tropical rainforest. After the Mayans abandoned their primary cities, the Yucatán peninsula became the principal region of a new culture called Toltec-Mayan, which was formed when Toltecs integrated with indigenous Maya peoples.
The Mayans focused on astronomical science and mathematics and were more advanced than most of the pre-modern world. Mayans also developed a highly sophisticated system of writing that was used to facilitate communication. A royal class lived in the cities of Mayan territories while the average population resided in small farming villages. Mayan religion was based on acclimating humanity to the cycles of the universe and the belief that the universe functions in a logical, cyclical and predictable way, and that human beings could exploit that cyclical nature.