Quaternions explained
Quaternions are a great way to represent rotations in the 3D space. They only require multiplications, without the use of any expensive transcedental functions.
Unfortunately, all of the texts I came across discussing quaternions only mention how to apply a quaternion for rotations in 3D, without truely explaining the thinking behind them. After some Googling I came accross a great YouTube lecture series discussing quaternions in detail, given by N. J. Wildberger, a pure mathematician at UNSW in Australia. For anyone interested in truely understanding quaterions I highly recommend watching the lecture series!
In case the relation between complex numbers and rotations in the plane as mentioned in the first lecture is not obvious for you, have a look at the WildTrig15 lecture, which explains this relation.