Rotations
Rotation, combined with translation and scaling, are the three affin transforms we do every day in the 3D nutshell universe. The rotation itself, however, is somehow much more complicated than the other two transform, it is one really needs a matrix representation among all three. Representations and computation of it has been developed for years. We have systems like Axis-angle representation, matrix representation, euler angles and quaternions. Despite I have known them for a long time, when I forgot, the rotation is still complicated. Here I am writing this again, as easily understanding as possible, for my future-self (or I can just travel through time to ask myself now).