Algebraic theory of numbers by P. Samuel
Does not seem to be available online via SU login (I'm told you can find it online if you look a bit harder)
Chapter 6 gives a concise introduction to how Galois theory enters in the arithmetic theory of algebraic numbers, via the decomposition and inertia subgroups of the Galois group, and how this is related to the splitting of primes in extensions.
Klicka på Algebraic theory of numbers by P. Samuel för att öppna resurs