The historic proof that polynomials of degree 5 or higher cannot generally be solved by basic arithmetic and roots.
The centerpiece of the chapter, establishing a one-to-one correspondence between subfields of a Galois extension and subgroups of its Galois group. 14.3 Finite Fields: Properties of fields with pnp to the n-th power elements and their cyclic Galois groups. Dummit And Foote Solutions Chapter 14
Introduction to the group of automorphisms of a field that fix a subfield The historic proof that polynomials of degree 5