David Eberly has written a huge amount of great and free intro mathematical papers. The "Mathematics/Algebra" section of [1] has a few things on quaternions, i

David Eberly has written a huge amount of great and free intro mathematical papers. The "Mathematics/Algebra" section of [1] has a few things on quaternions, including a nice self-contained linear algebra-based derivation of why it makes sense to represent a rotation with four numbers, which ends up being a sneaky introduction to quaternions [2] [1] https://www.geometrictools.com/Documentation/Documentation.html https://www.geometrictools.com/Documentation/Documentation.h... [2] https://www.geometrictools.com/Documentation/LinearAlgebraicQuaternions.pdf https://www.geometrictools.com/Documentation/LinearAlgebraic...