I'm looking to read more about Native American culture especially about rituals, mythology and daily life.
Which native Americans? That's a huge geographical region to cover. Even if we limit things to the continental United States, you'll still find incredible diversity of culture; the Lakota are nothing like the Navajo, the Mohawks are nothing like the Choctaws, and so on.
For a more emic / critical perspective, possibly Vine Deloria's God is Red. American Indian Studies Research Institute also has some oral history based texts. I am more familiar with the indigenous studies side of native american literature, but ... look at authors like Louise Erdrich, Joy Harjo, Leslie Marmon Silke and read who they read/cite.