I'm assuming you mean the main points of the Aztec worldview. In the 15th century Aztec religion and worldview was a mix of their own beliefs and things gleaned from other cultures in Mexico. Abandoned older cities such as Teotihuacon and other Toltec and Olmec sites were considered sacred, and the Aztecs copied their architecture and put objects they believed to have been sacred in their own temples.
The calendar is the aspect of Aztec culture most popularly studied today. There were actually two calendars, the xiuphohualli of 365 days involving the seasons and solar time, and the tonalhopualli or "day-count," the sacred calendar of 260 days. The day-count runs on a system of thirteens, and interacts with the solar calendar concurrently and in a complex relationship. The day-count and solar calendar run so that every 52 years the count of years begins again.
The day-count divides the days among rituals to the different Aztec gods, who are considered to always be in perpetual action against or with one another. The cosmos is seen as a continual struggle which is never "won" or "lost" in the end, simply continuing motion. No gods or goddesses are "good" or "evil", just different. Conflict is seen as necessary, with the universe balanced between opposites. Things are seen as light or dark, in varying degrees, not "black and white," with both light and dark necessary.
The Aztec viewed the universe as consisting of multiple layers, but circular, not horizontal. The layers are contained within one another, rather than in layers atop each other. The layer humans inhabit is between the Heavens and the Underworld, and in fact is seen as the lowermost layer of Heaven and the uppermost of the Underworld. Our layer is both because here there is both life and death. The layers of stars and planets are "above" us, so to speak, and then more layers leading outward to Omeyocan, the "Place of Duality." This is where Ometeotl lives, the Divine Duality. Viewed as pure divinity, not a personified god, it is sometimes represented as Lord and Lady Duality, Ometecucuhtli and Omecihuatl, from whose union are born the gods and goddesses. Those gods and goddesses inhabit various other layers of Heaven. In the opposite direction from our world are the layers of the Underworld, leading to Mictlan, the Place of the Dead.
The Aztec worldview influenced the Aztec people's beliefs that their gods needed to be appeased. Their view is that their gods sacrificed themselves in the creation of the world, so they needed sacrifices to be repayed. Please review Hi1954's response for the details on the calendar and how their cosmology influenced their beliefs.
The Aztec number one crop was Maize which is a heavy nitrogen feeder, so as times grew hard in corn production, more sacrificial victims were needed to please/appease the gods. The Aztecs also grew corn on reed mats in manmade lakes. As their population grew, they needed more land area on which to grow corn.
The Aztecs chose their victims normally from conquered warriors who may have held similar beliefs. The victim was picked usually 20 days before the sacrifice and as far in advance as a year. For that period of time, the sacrificial victim dressed as the god to whom he would be sacrificed. The Aztecs believed that the god actually entered the victim at the time of sacrifice. The "flowery death" upon the altar alludes to the fountains of blood that pulsed out of the victim's chest at the time of the sacrifice. The Aztecs believed that death as a sacrifice guaranteed the victim a place in the "house of the Sun". This would be considered a high honor.
All of this human sacrifice and warfare did not endear the Aztecs to their neighbors. When the Spaniards came to the New World, the Aztecs saw them as their gods come to life. They had supernatural abilities (guns and gunpowder, horses, and metal hats) (See this excerpt.) The effect on the Aztecs was dire, they were conquered and enslaved. They suffered the ravages of European diseases to which they had no immunity.
I agreee with you, that god does not exist because of evolution and the big bang. but i don't agree with u about the Aztecs being barbarians, killing humans. the main reason that has happened is becuase they did not know what human sacrifice was. u know what i mean right. they thought god was the ultimate supreme, and god is the most important thing in the world. that's why they made big temples to get them physically closer to the gods. they thought if they did not nourish gods with blood, he will grow sick and die. and there will be no sun rise. so they thought blood sacrifice was an essential part of there lives.
aztecs where the most sick minded hypocrytes ever to walk the earth i mean common what kinda sicko kills people for a god??? and one that donsn't even existe??? :)