One unknown of first and second degree tends to be studied in detail in high school level algebra. In order to solve algebraic equations we gain the knowledge regarding general formulae intertwined with coefficients utilizing arithmetic operations and radicals. The problem arises when attempting to uncover general formulae in regards to algebra of a greater
difficulty level than one taught in high school. General formulae is also known to exist for algebraic equations of the third and fourth degree. In this preface to these series of articles regarding equations involving Abel’s theorem, you fill find the general formulae used for solving algebraic questions of the third and fourth degree in the introduction. Despite this, the generic equation typically used for the lower 4 degrees does not apply to the unknown higher degree and it’s equation cannot be solved by radicals, as there is no general formulae that expresses the roots of these equations pertaining to their coefficients utilizing arithmetic operations as well as radicals. This is what Abel’s theorem proposes.

The purpose of these series of articles is to spread awareness as to the existence of this theorem. Despite this, we will not go into the work of French mathematician Evariste Galois. In his work, special algebraic equations such as having certain numbers as coefficients, and it is with these equations that began the conditions whose roots were used to represent the terms of coefficients through the ways of algebraic equations and radicals. Interestingly, Galois’s findings can be deduced to find the Abel theorem. In these series of articles we will explore the contrary, and through this are capable of inquiring about two branches of mathematics, which are group theory and the theory of functions of one complex variable. We will examine the properties of a group and a field. We will also examine the nature of complex numbers and why they are called as such. We will also examine the Riemann surface in addition to being able to eventually define the basic theorem of the complex numbers algebra.