Solving Solvable Quartic, Quintic and Sextic Equations

This thesis contains the result of K. Conrad, D. S. Dummit and T. R. Hagedorn about solving solvable polynomials of degree 4, 5 and 6 using Galois theory. First of all we will describe a procedure for figuring out the Galois groups of separable irreducible quartics (we are not going to derive the classical quartic formula by Ferrari). Then we will give general formulas for finding the roots of all irreducible quintic (sextic respectively) polynomials f(x) ∈ Q[x] with Gal(f)= Gf , where Gf is a transitive, solvable subgroup of S5 (S6 resp.).