I'm currently working through Naive Lie Theory https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Math... by Stillwell and there's a lot about quaternions in the first chapter, including their standard matrix representation. You'd need to be familiar with some group theory to fully understand the 3D rotations but the matrix operations are clear enough to start coding with, I think.

Stillwell[1] discusses quaternions in chapters 1 & 2, although the meat and potatoes of the book is more generally about lie groups and lie algebras. It's pitched at a lower level than most books on this topic by restricting attention to the classical matrix groups.

[1]https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Math...

http://www.amazon.com/Naive-Theory-Undergraduate-Texts-Mathe... is quite readable