Over the summer, I've been in the opposite situation as you (an American reading up on indigenous Australian history and culture). It's been challenging to find appropriate material here in the States; hopefully your search won't be as difficult but to make it a bit easier, I'll be sticking with books that are likely to be readily available.

Others have already recommended Charles Mann's 1491. It'll give you a broad basic introduction to the indigenous history of the Americas around the time of initial European contact. You may also be interested in its sequel 1493, which discusses how the establishment of trans-Atlantic contact effected the world at large.

From here, I'll only be discussing works that focus on the area that is now the United States, mainly east of the Mississippi River and prior to the Indian Removal Act (which is an immensely important and tragic event in the history of the region).

• The Moundbuilders: Ancient Peoples of Eastern North America - this book will give you a basic introduction to the major "moundbuilding" cultures, from Poverty Point nearly 4000 years ago to the Mississippians cultures at the time of European contact. Earthworks are a significant architectural feature in this part part of the world and include gigantic pyramids, observatories, ceremonial grounds, burials, enormous animal effigies, defensive structures, etc.

• Cahokia: Ancient America's Great City on the Mississippi - Cahokia was among the largest, if not the largest, city north of Mexico until about the 1800s. Timothy Pauketat is one of the leading authorities on the site and has written many books about it; this is the most accessible and available.

• The Iroquois - The Haudenosaunee, more famously known as the Iroquois Confederacy, are one of the most prominent Native nations in eastern part of the continent and this book covers 1100 years of their history. A point of debate on this topic however: Dean Snow favors a late pre-Columbian / early post-Columbian date for the founding of the confederacy (1451 or 1536), while others favor an early date in 1142. There are a lot of other books on the Iroquois available and you might have better luck finding some of those. If you can't get Snow's book, try for Iroquois Diplomacy on the Early American Frontier and /or The Ambiguous Iroquois Empire. Also look for Iroquoian Women, which will give you a different perspective that the typically male-oriented histories.

• The American Revolution in Indian Country, The Shawnees and the War for America, The Victory with No Name, and really anything by Colin Calloway. The three books listed here will cover the transition during the independence of the United States. The first discusses how the Revolution affected eight different Native American communities from New England to Florida, the second discusses the Shawnee resistance to colonialism from the French and Indian War in the mid-1700s to Tecumseh and the War of 1812; the third focuses on the Northwest Indian War and the crushing defeat dealt to the United States by indigenous forces.

• Creek Country - The Creek Confederacy arose out of alliance of four old Mississippian polities, accumulated additional members, and eventually controlled most of what is now Georgia and Alabama. This book is mainly concerned with their history in the late 1700s and early 1800s. Try to find A Sacred Path as well; it'll introduce you to Creek religious and philosophic topics.

• Cherokee Women and The Cherokee Nation and the Trail of Tears - while the Cherokee were not the only nation to suffer because of the Indian Removal Act, their Trail of Tears is the most iconic. The first covers changes in Cherokee culture beginning with European contact and leading up to Removal, with special emphasis on how this transition affected women; the second covers the history of the Cherokee Removal itself.

And, of course, you can always ask specific questions here.

To specialists who pop into this post, how well has Dee Brown held up over the years? Bury my Heart at Wounded Knee is an amazing book, and I've heard that in recent years some of his more controversial assertions in the book have been validated, but as a non-specialist I'm curious what contemporary academia thinks.

I'm just a layman, but I'm currently reading a book I saw recommended in this sub - 1491: New Revelations of the Americas Before Columbus. I'm finding it fascinating and engaging!

Pekka Hamalainan's Comanche Empire is a great read on the post-contact history of the American West that posits the Comanche in the Southwest (Texas, New Mexico, Colorado) as a sophisticated empire whose power rivaled that of the United States and Mexico in the region. It's an excellent an innovative piece of scholarship.

The Last Indian War by Elliot West. Its very informative and its an easy read. Almost flows like a novel. Its focus is not on native culture specifically, but the culture and its impact on the Nez Perce conflict with the american government/people plays a central role. I really cant recommend it highly enough.

I'd recommend Black Elk Speaks as another option. It's a very stirring and sad story, but it demonstrates how badly Europeans understood Native Americans.

The Inconvenient Indian by Thomas King is the go-to, and it will give you far and away the best overview out there. Here is a response I gave to a question on American Indians a while back which is essentially pulled from this book. If anyone knows of a better source out there, please let me know.

I saw someone ask about Bury My Heart at Wounded Knee. I think it's still worth reading, but be aware that it focuses on American Indians almost exclusively as victims whose culture was essentially lost. But as tribes all over the US and Canada are showing us, their cultures remain and - much like any other culture - have transformed over time and in light of new circumstances but are still distinctly Indian. Should you read it, King's work will illuminate this point very well.

I also saw mention of 1491, which I agree is absolutely worth reading. If you have access to academic databases, I would also recommend looking into William Cronon who seems to me a major influence on Mann. He wrote a really good environmental history in the 80s called Changes in the Land which covers relationships between colonists, Indians, and the land in New England. It's very specialized and academic, but is important as the first environmental history of its kind. But his overall views (especially in challenging environmental determinism) can be found in much shorter articles.

For more recent Navajo history, the book The Navajo People and Uranium Mining and the movie The Return of Navajo Boy are both good resources. My professor is one of the authors on the former.

Oh, and the National Museum of the American Indian puts a lot of its stuff online.

Anasazi America by David Stuart. It covers the rise and fall of the Chaco Anasazi in the Southwestern US. Really good read.

Don't remember the author, but Blood and Thunder was an awesome history of later settlement/war with natives.