The Abel-Ruffini Theorem : The insolvability of the general quintic equation by radicals

Abstract: This thesis explores the topic of Galois theory at a relatively introductory level with the goal of proving the Abel Ruffini theorem. In the first part algebraic structures are considered: groups, ring, fields, etc. Following this, polynomial rings are introduced and the attention is then turned to finite field-extensions. In the final section of the main text solvable extensions are studied and the Abel-Ruffini theorem is proved. The discussion section gives a brief overview of analytic methods of solving polynomial-equations.