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They had irrigation systems, terracing and farming skills, created complicated calendars (an advanced understanding of seasons/astronomy), and written language. They had advanced math skills (geometry and the metric system, even trigonometry) judging by the engineering/architecture of their cities/buildings. (They used pulley systems like a modern day crane).

Their culture was highly advanced in that they had a set governmental hierarchy, political system, religion, rules/laws, social roles, and even leisurely sports. They had military prowess and understood how to advance their culture through warfare.

They were highly accomplished craftsmen and made pottery, wheeled toys (though they didn't use the wheel for anything else), weaved baskets, clothes-making (clothes and jewelry were even used to symbalize social status), dye-making, etc.

They traded with surrounding nations and had trade routes between other leading nations.

They were, in every way, an advanced civilization/society because they could create and wield their own tools and manipulate their environment to suit their needs.

@ ammianus: The Spanish beat them with their plagues not their military tactics. Most natives were killed from European diseases. The Spanish only beat them because they outnumbered the natives following the plague epidemic.

Socially very advanced,with large cities and a well organized government and social hierarchy.

However,technologically they were all stuck in the Stone Age;even the Incas and Aztecs hadn't gotten around to inventing the wheel by 1500 (and for those that say they didn't need it,the application of the wheelbarrow to the agricultural sytems that were the centre of both civilizations makes the wheel worth inventing just for that).

So,perhaps not so advanced after all - if they were,a handful of ignorant Spanish adventurers wouldn't have been able to defeat and conquer them so quickly and so comprehensively.

Edit:

Gemi,look at the battle of Cajamarca 1532,where Pizarro and his 168 Spaniards defeated thousands of Incas - well before any disease epidemics decimated the Inca population,and the Spanish can hardly be said to have outnumbered the Inca in this battle.The lowest populstion estimate for the INca empire is 4 million,so even after 90% of them had died from disease,that leaves 400,000 - which is a far bigger number than 168.

Lowest estimates for the Aztecs population are 5 million - leaving 500,000 after disease did for 90% of them,which is a much larger number than the 1400 or so Spaniards Cortes had under his command.Even adding in native allies,Cortes was still heavily outnumbered by the Aztec armies in the field.

So,your assertion that the Spaniards defeated the Inca and Aztecs because they outnumbered them after disease had taken its toll is nonsense.The Spaniards won militarily because they had steel armour (against which Stone Age weapons shattered) and steel edged and bladed weapons (which sliced through the feather shields and animal pelt uniforms of Aztecs and Incas) and because they had firearms - in short,because technologically they were far more advanced.

The Aztecs, Mayans, and Incas rules their cowed populations with religion and fear which killed thousands, a fact which put them all on an equal standing with the "advanced" European elites who did exactly the same thing.

yes---the Mound-builders, Incas mayans, Aztecs , Hopi and Cherokee, to name a few.

Depends how you define "vary advanced."

I'd say the domestication of corn, the Aleutian Kayak, and Mayan Calender are the peak accomplishments.

Advanced civilization is a strong phrase...but I suppose the architecture of their temples or Macchu Piccu (botched the spelling there, I know) could count.