Well, as the title says I would like to know a good and direct book about Galois Theory (and also that apllies the theory for the study of polynomials). It's been kinda impossible for me to find such one, since I have tried a few books (non-intuitive and non-direct, one of them was a Thomas Hungerford's) on this theory.
About the other question: I know that there are no solutions in radicals of higher than 4 degree polynomial equations, however, I have seen these questions: Trigonometric solution to solvable equations and Does this higher-order polynomial have an analytic solution?. So, my question is:
And what about the unsolvable ones? We can only find the roots through numerical methods? Also, which books about this would you recommend me reading?
Concerning Galois theory, I suggest Jean-Pierre Tignol's Galois' Theory of Algebraic Equations.
And concerning the solution of higher degree equations, I suggest Jerry Shurman's Geometry of the Quintic.