
Chapter 1
Classical Algebra
In the first part of this book, Chapters 1-15, we present a (fairly) modern version of
Galois’s ideas in the same setting that he used, namely, the complex numbers. Later,
from Chapter 16 onwards, we generalise the setting, but the complex numbers have
the advantages of being familiar and concrete. By initially restricting ourselves to
complex numbers, we can focus on the main ideas that Galois introduced, without
getting too distracted by ‘abstract nonsense’.
A warning is in order. The decision to work over the complex numbers has advan-
tages in terms of accessibility of the material, but it sometimes makes the discussion ...