Lecture 1 - Historical Perspectives

Lecture 2 - Examples of Fields

Lecture 3 - Polynomials and Basic properties

Lecture 4 - Polynomial Rings

Lecture 5 - Unit and Unit Groups

Lecture 6 - Division with remainder and prime factorization

Lecture 7 - Zeroes of Polynomials

Lecture 8 - Polynomial functions

Lecture 9 - Algebraically closed Fields and statement of FTA

Lecture 10 - Gaussâ€™s Theorem(Uniqueness of factorization)

Lecture 11 - Digression on Rings homomorphism, Algebras

Lecture 12 - Kernel of homomorphisms and ideals in K[X],Z

Lecture 13 - Algebraic elements

Lecture 14 - Examples

Lecture 15 - Minimal Polynomials

Lecture 16 - Characterization of Algebraic elements

Lecture 17 - Theorem of Kronecker

Lecture 18 - Examples

Lecture 19 - Digression on Groups

Lecture 20 - Some examples and Characteristic of a Ring

Lecture 21 - Finite subGroups of the Unit Group of a Field

Lecture 22 - Construction of Finite Fields

Lecture 23 - Digression on Group action - I

Lecture 24 - Automorphism Groups of a Field Extension

Lecture 25 - Dedekind-Artin Theorem

Lecture 26 - Galois Extension

Lecture 27 - Examples of Galois extension

Lecture 28 - Examples of Automorphism Groups

Lecture 29 - Digression on Linear Algebra

Lecture 30 - Minimal and Characteristic Polynomials, Norms, Trace of elements

Lecture 31 - Primitive Element Theorem for Galois Extension

Lecture 32 - Fundamental Theorem of Galois Theory

Lecture 33 - Fundamental Theorem of Galois Theory (Continued...)

Lecture 34 - Cyclotomic extensions

Lecture 35 - Cyclotomic Polynomials

Lecture 36 - Irreducibility of Cyclotomic Polynomials over Q

Lecture 37 - Reducibility of Cyclotomic Polynomials over Finite Fields

Lecture 38 - Galois Group of Cyclotomic Polynomials

Lecture 39 - Extension over a fixed Field of a finite subGroup is Galois Extension

Lecture 40 - Digression on Group action - II

Lecture 41 - Correspondence of Normal SubGroups and Galois sub-extensions

Lecture 42 - Correspondence of Normal SubGroups and Galois sub-extensions (Continued...)

Lecture 43 - Inverse Galois problem for Abelian Groups

Lecture 44 - Elementary Symmetric Polynomials

Lecture 45 - Fundamental Theorem on Symmetric Polynomials

Lecture 46 - Gal (K[X1,X2,â€¦,Xn]/K[S1,S2,...,Sn])

Lecture 47 - Digression on Symmetric and Alternating Group

Lecture 48 - Discriminant of a Polynomial

Lecture 49 - Zeroes and Embeddings

Lecture 50 - Normal Extensions

Lecture 51 - Existence of Algebraic Closure

Lecture 52 - Uniqueness of Algebraic Closure

Lecture 53 - Proof of The Fundamental Theorem of Algebra

Lecture 54 - Galois Group of a Polynomial

Lecture 55 - Perfect Fields

Lecture 56 - Embeddings

Lecture 57 - Characterization of finite Separable extension

Lecture 58 - Primitive Element Theorem

Lecture 59 - Equivalence of Galois extensions and Normal-Separable extensions

Lecture 60 - Operation of Galois Group of Polynomial on the set of zeroes

Lecture 61 - Discriminants

Lecture 62 - Examples for further study