This. If you only want to understand *how to apply* quaternions to represent rotations, it's not too hard to learn. However, if you want to understand *why* they work, that's a totally different story.

Many of my colleagues still use Euler angles to represent rotations. I always use quaternions, and am a bit baffled why people are so averse to them.

Quaternions are the generators of SU(2) which is a double covering of SO(3). The latter describes rotations in 3 dimensions. Thus you can express any rotation in 3d with quaternions.

The idea is that quaternions are the wrong way to look at the problem and that a better approach would be to use geometric algebra, bivectors and rotors. The formulas are essentially the same as with quaternions, but at least for me, this approach make more intuitive sense. It also work in dimensions other than 3, which matter to the author as he is the author of "4D toys" and hopefully, Miegakure.

Here is another talk on the subject, by a different author: https://www.youtube.com/watch?v=htYh-Tq7ZBI It is not specifically about quaternions, it is about multiplying vectors and what you get from that, and it includes quaternions.