- Understanding of the role of groups for the solution of algebraic equations in one unknown
- Understanding of the relation between equations and field extensions
- Being able to use the Galois correspondence between subgroups and intermediate fields
- Being able to determine the Galois group in simple cases
- Understanding of the solvability of equations in terms of Galois groups
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- Automorphisms of field extension, the Galois group
- Normal extensions and splitting fields
- The main theorem of Galois theory
- Cyclotomic extensions and polynomials
- The Galois group of a polynomial
- Equations over the rationals, in particular reduction modulo a prime
- Solvability of groups and equations
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