This Lecture Notes is one semester course on some advanced topics of abstract algebra of M.Sc. Programme in Mathematics. This Lecture Notes teach the development from ring theory to Galois theory as a rigorous mathematical subject. The basic ingredients of this Lecture Notes are Euclidean ring, polynomial rings, extension fields, Galois theory. Proofs of all concerning results are given with students friendly manner. Sufficient number of examples are given to digest theory.
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