Modules over PIDs: Basic theory, Structure theorem for finitely generated abelian groups, Rational and Jordan canonical forms.

Field Theory: Algebraic extensions, Splitting fields, Algebraic closures, Separable and Inseparable extensions, Cyclotomic polynomials and extensions, Galois extensions, Fundamental Theorem of Galois theory, Finite fields, Composite extensions, Simple extensions, Cyclotomic extensions and Abelian extensions over rational field, Galois groups of polynomials, Fundamental theorem of algebra, Solvable and Radical extensions, Computation of Galois groups over rational field.