The lectures start with a brief guide through the classical Galois theory, with special emphasis put on:
(a) formulation of Galois extenions of fields in the way that lends itself naturally to non-commutative generalisation;
(b) geometric meaning of Galois extensions.
In the second part, the theory of Galois extensions of non-commutative rings (algebras) known as Hopf-Galois extensions is presented leading to the interpretation of such extensions as principal fibre bundles in noncommutative geometry.