Curiously, the museum has gathered artifacts from all the South and Central American civilizations, not just from the Andes. But most of the textiles were from Peru and Chile. I don't know enough about the various peoples and empires that succeeded each other in the pre-Columbian eras to distinguish among them, so I'll dispense with the geographical identifications and just tell you the dates.
Much of the Andes mountains is desert, and the low humidity has contributed to the remarkable longevity of these textiles. Considering how enthusiastically my jeans fray and disintegrate at the hem and how frequently I encounter a rotten piece of cloth in a flea market or old box, I am always amazed to see fabrics and garments that have hung on for millenia. Perhaps because the Inca didn't treat their yarns with formaldehyde for wrinkle-resistance.
I don't know enough about weaving to appreciate the nuances of technique, but I can savor the richness of the colors, the uniformity of the weave, the intricacy of the pattern. My photos may be marred by reflections from the glass, but I think you'll share my wonder and delight at these specimens.
funeral cloth, llama yarn 500-700 AD