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.