Q:

Classical Impossible Constructions of Geometry proofs with Abstract Algebra.

Trisecting an angle (dividing a given angle into three equal angles),
Squaring a circle (constructing a square with the same area as a given circle), and
Doubling a cube (constructing a cube with twice the volume of a given cube).

Told that these problems could only be proved with abstract algebra.  I have no idea how to start.  I have found this page. 
I have an idea of what is being said, but no idea about how to exactly prove this.  Any pointers would be helpful. 

A:

Field theory and its classical problems by  Hadlock is a wonderful book motivated by these problems.
See also Geometry: Euclid and Beyond by Hartshorne.

