## § Galois theory by "Abel's theorem in problems and solutions"

I found the ideas in the book fascinating. The rough idea was:
- Show that the $n$th root operation allows for some "winding behaviour"on the complex plane.
- This winding behaviour of the $n$th root is controlled by $S_n$, since we arecontrolling how the different sheets of the riemann surface can be permuted.
- Show that by taking an $n$th root, we are only creating solvable groups.
- Show tha $S_5$ is not solvable.