Check out Charles Mann's 1491: New Revelations of the Americans Before Columbus. It's a popular book, but a tremendously good read and well-respected by the experts. It does as much as I have seen towards answering your question in an accessible and gripping way, with a minimal of academic in-fighting and jargon. Some of these things are very difficult to do because of source limitations — the Inca, for example, had no written language, and so our record of what their "science, culture, philosophy" would have been is pretty sketchy. Mann does it a good job of presenting what we have.

For the Incas specifically I would recommend looking into either Craig Morris' and Adriana von Hagen's "The Incas", or Terence D'Altroy's "The Incas". Both are good overviews of Inca society, empire, and history.

More broadly to Andean prehistory in general (and expanding our data to include archaeology as well as history, since we have no historical record-keeping that we can read in the Andes), check out Jeffrey Quilter's "The Ancient Central Andes", Jerry Moore's "A Prehistory of South America"; and for a treatment of early Andean social complexity, Richard Burger's "Chavin and the Origins of Andean Civilization".

Happy to respond with more suggestions if you have more specific questions!