I would like to learn more about the pre-Colombian history of the native tribes of North America, particularly the Iriquois, Cherokee, and Lakota Sioux. What books should I read?
If I had more time, I could give you a more complete list of suggestions, but I'll have to be brief for now (after the weekend, I may revisit this topic). The Smithsonian Handbook of North American Indians can be hard to come by, but if you're in a university setting you might have access it. It's worth checking out. The Blackwell series is a good place to start. Notably Dean Snow's The Iroquios and Guy Gibbon's *The Sioux: The Dakota and Lakota Nations." Sadly, Gerald Schroedl's The Cherokee, which was intended to be part of this series, never materialized. Luckily, there's Theda Purdue's Cherokee Women: Gender and Culture Change, 1700-1835, which is a great book on the evolving nature of Cherokee culture (particularly gender dynamics) prior to Removal. Also, look into George Milner's The Moundbuilders: Ancient Peoples of Eastern North America.
/u/Reedstilt mentions excellent sources, as usual.
You may also want to go to the tribes themselves - most modern Native tribes have websites that talk about their history. Many tribes, like the [Eastern Band of Cherokee Indians] (http://www.cherokeemuseum.org/), also have museums that go extensively into tribal history.