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It is a tool of extraordinary beauty, used for a task of extreme brutality. The handle is worked in turquoise, shell and chalcedony to form a crouching man; the blade is a leaf of white flint. With this sacrificial knife, Aztec priests tore out the hearts of living men — offerings meant to appease the gods. With its superb form and savage function, the knife embodies the essential duality of Aztec civilization.

The two faces of this vanished culture come under scrutiny in "Aztecs," an exhibition of 359 objects of art and sculpture at London's Royal Academy of Arts through April 11. With Western artists making increasingly feeble attempts to shock, it is a frankly redemptive experience to immerse oneself in a vanished culture that embraced the dark side of existence in all its paradox and mystery, and celebrated the horrible with as much enthusiasm as it did the joyous.

The Aztecs mercilessly slaughtered their prisoners of war, but they also wrote poignant verse lamenting the transience of life. Their society was ordered: adultery and drunkenness were frowned upon. But it was perfectly acceptable to butcher a child in honor of some fearsome god.

When not offering human sacrifice, priests studied the stars, discussed philosophy and educated the children of nobles. And their rich cosmology rejoiced in dichotomy. The goddess of childbirth was simultaneously the deity of filth and purification: she devoured dirt and wrongdoings.

The art on show takes in these extremes — tender images of men and women, outsize stone insects and snakes, fruit carved out of semiprecious stones, skull-faced deities with necklaces of severed hands, and a sacrificial altar to supply the gods with the necessary tribute in human blood. One of the 11 rooms given over to the exhibition is dedicated to the gods of life, among them the oddly grim god of spring, Xipe Totec.

To symbolize death and rebirth, his priests wore, like him, a suit of flayed human skin, including the face. And just wait until you meet the gods of death, like the fearsome Mictlantecuhtli, the bright-eyed, skeletal ruler of the underworld, where the sun fights every night to be reborn. He is represented, teeth bared, on the side of an alabaster urn.

Aztec artists worked with a wide range of materials, including terra-cotta, gold, stone, turquoise and shell. They painted their human figures in lifelike colors and may even have dressed them in costume.

Some have clothes carved in detail: plaits, ponchos and ceremonial paper head-dresses. The Aztecs also used pictogram writing to record their lives and the religious calendar in illustrated books of deerskin and tree bark.

When they arrived in the area in the 16th century, the Spaniards overwhelmed — and then tried to obliterate — Aztec culture, smashing down buildings and using stones from the Great Temple of Tenochtitlan, the fabulous Aztec capital on the site of what is now Mexico City, to build a cathedral nearby. The temple was thought lost, but was rediscovered in 1978 by workers carrying out routine maintenance work. Archeologists have been mining the site ever since, and coming up with exquisite finds, many of which are on show in London. Fragments from the temple's decoration — such as a giant stone rattlesnake head — hint at its magnificence. Over 100 offerings to the gods were turned up, and a complete stone casket of gifts can be seen as it was found.

In 1980, a life-size clay Eagle Man was discovered in the ruins. At first sight, it seems to be another fantastic deity, an avian-human hybrid. But closer inspection reveals it to be a human in ritual garb: Aztec priests impersonated their gods, wearing their skins and regalia in elaborate rites. A man in a bird costume shows up in a sketch from the Codex Azcatitlan, a group of scenes of the Aztec past, that depicts the conquering Spaniard Hernán Cortés arriving at the Great Temple. The Spaniards destroyed many of the Aztecs' books, but they also collaborated to produce new ones. Missionaries persuaded the conquered people to copy ancient texts explaining their customs, and wrote commentaries in Spanish and Nahuatl, the local language. In one such project, the Codex Magliabechiano, a copy of a pre-Hispanic book illlustrating beliefs and rites, a memorable sketch shows Aztecs offering bowls of human blood to Mictlantecuhtli, the king of terrors.

In 1994, Mictlantecuhtli himself emerged from the temple ruins. A life-size clay image shows him half flayed, half eviscerated. The butchered god lived with his consort on the lowest plane, a region of damp and cold. But the rulers of hell mirrored a heavenly couple, and the underworld was also the universal womb. If we see with the Aztecs' eyes, everything contains its opposite.

• Aztec art combined beauty with terrifying function — and a clear vision of the dark side of existence