Galois Groups and Field Extensions for Solvable Quintics : Analysis of irreducible and reducible polynomials of degree 5

In the context of self-studies on polynomials of degree 5 (quintics), Galois groups and field extensions related to solvable quintics - irreducible and reducible ones - have been analyzed. Effort has been spent to provide comprehensive explanations and some examples of those structures; the intention is to give the reader an overview and a decent insight into the topic, which may help to understand the algebraic structures and their arithmetics better.