The purpose of this course is to give informations about field extensions and Galois theory, and to examine the fields that contains roots of polynomials and the polynomials that admit elements of field as its roots, and to improve the ability of abstract thinking and to give ability to establish relationships between this course and the other areas of mathematics.

Field Extensions, Splitting Fiedls and Algebraic Closure, Field Isomorphisms and Extensions, Seperability, Finite Fields, Galois Theory, The Galois Group of a Polynomial, Cyclic Extensions, Cyclotomic Extensions.