@anakhro Hm, motivation for some of the exercises,also:
Group Actions have no chapter - just 5 short exercises. And they are not shown as homomorphisms from a group to a subgroup of Sym(X), but they are just shown as the image in Sym(X). Ie. an action on X is a subgroup of Sym(X), also the notation is not $x \cdot y$ but just $y(x)$ which is not that horrible, but it's annoying cause it's less popular
So in all practicality - I can't seem to use the Orbit Stabilizer Theorem for anything useful, like say proving Cauchy's Theorem.