When we can find the solutions for a polynomial with rational coefficients using only rational numbers and the operations of addition, subtraction, division, multiplication and finding nth roots, we say that p(x) is solvable by radicals. The main content of this course is to introduce Galois theory and then to study of what conditions a polynomial is solvable by radicals. The related topics in abstract algebra are organized as follows.

1. Group Theory:
Groups; Normal subgroups and Quotient groups; Solvable groups; Group action and Sylow theorems; The fundamental theorem of finitely generated abelian groups.

2. Ring Theory:
EDs, PIDs and UFDs; Polynomial rings.

3. Field Theory:
Field extensions, the Fundamental theorem of Galois theory, Finite fields, Solution by radicals, Abelian extension, Kummer extension, Calculations of Galois groups.