I'm currently taking world history and learning about this part, but it seems like the textbook we use only talks about the 4 river valley civilizations. I'm really curious about what's happening in other parts like South America and etc.
This is difficult to answer as it is incredibly broad; Sumer, Pre-Dynastic Egypt, Harrapan civ, and the Chinese civs were hardly contemporaneous and "the rest of the world" is an awful lot of space. Is there any particular place you're interested in?