The course consists in a classical exposition of Galois Theory. In the first part we’ll develop basic concepts and methods of group theory and rings, in particular group actions, solvability and the classification of finitely generated modules on a principal ideal domain. In the second part we’ll apply this machinery to galois duality to prove Galois criterion of solvability. 
Detailed programme:
Ruler and compass constructions. Group actions, G-sets, First Homomorphism Theorem for G-sets, orbit equation, nilpotency of finite p-groups, Sylow’s theorems, solvable groups, Fitting’s theorem, finitely generated modules over a principal ideal domain, fundamentals of Galois theory, Galois extensions, separability, and pure inseparability, finite fields, Galois criterion for solvability by radicals.