In this chapter, we present 100 problems without solutions (but occasionally with some hints, comments or references). These are original, interesting or challenging problems covering various aspects of Galois theory. Several of these problems can be used as a starting point for student projects, such as problems related to the normal core of groups, Galois index, the notion of elements of field extensions essentially defined over a subfield. Some of the problems are suitably structured in order to introduce some interesting topics that are typically not covered in standard texts on the subject, incl. Dedekind’s duality, Tschirnhausen’s transformations and the lunes of Hippocrates.
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