This is a difficult question to answer on several counts. US history is one thing, but global history encompasses pretty much everything we cover on r/AskHistorians. If you let us know which aspects of global history interest you most, people would be able to make some more specific suggestions for you. You should also check out our booklist which is organised by subjects, time periods, and geographical regions.

It's also tricky to answer your question because you haven't said which types of history interest you most. Do you like military history? Social history? Cultural, religious, economic, or political history? That would really help us address your interests more specifically.

The third thing that would be helpful to know is what your background is in asking this question. I'm going to try to make some US history reading suggestions for you based on the assumption that you are US-educated, which is why you separated out the US from other parts of the world. So I will make recommendations based on the idea that you may have been taught US history but want to know more about what isn't taught in school.

My first recommendation in that vein would absolutely be Why You Can't Teach United States History Without American Indians edited by Susan Sleeper-Smith. This is an excellent book aimed at college professors who teach US history survey courses, but it's accessible to the general reader. Each chapter takes a different concept or time period in US history - such as mapping the country's expansion or the Civil War - and reframes it from the perspective of Native peoples. You may have learned about the fur trade in school, but did you know that guns and alcohol were only a tiny minority of what Native peoples traded fur for? We could just as well call it the "cloth trade" because that's what the Native peoples mostly wanted, and the textile industries of England and France competed to satisfy the Native American consumer market.

That's an example of the sort of eye-opening change of gears that this book injects into a conventional survey of US history. I'd highly recommend this book to anyone who wants to learn more about the history of the US, including how that history has been shaped to form settler-colonial narratives while leaving out huge chunks of the story. Every chapter is mind-blowing and will make you rethink the history of the US.

If you're interested in cultural history, I'd also recommend Native North American Art by Janet C. Berlo. This book provides a great overview of the different artistic traditions of the US and Canada, going from prehistoric times to the end of the 20th century. It's a really great book because it grounds Native cultural developments in historical change, rather than presenting the work of Native artists as timeless expressions of a "primitive" culture. You'll get to know lots of different Native artists and see how they used their art to respond to the huge historical changes going on around them, both before colonization and afterwards.

Those are my two best recommendations for overviews of US history. Without knowing in more detail what your particular interests are, it's hard to recommend anything more specific. There are as many ways to answer your question as there are readers on r/AskHistorians, but if you give us some more specific interests I'm sure plenty of other people could chime in with useful recommendations for you.