An Exploration of Galois Theory with some Classical Results

Abstract: Galois theory unites field theory and group theory to solve some field theoretical problems. The aim of this thesis is to provide a concise introduction to the topic, culminating in the proof of the insolubility of the general quintic equation by radicals. Using the developed field theory, a short discussion about geometric constructions is included, in which the impossibility of duplicating the cube, trisecting the angle and squaring the circle is shown.