At my university there is a debate about whether it is better to require students to have taken a class in Galois theory or to require a class in representation theory for admission into the graduate program. Currently, Galois theory is required for admission and rep theory is not. Many of the professors have argued that representation theory has a broader application and hence should be preferred over Galois theory on admissions applications. There are of course important links between the two topics, so I wanted to see what people at other universities have found to be more helpful in graduate school.
At my university, we teach Galois theory out of Dummit and Foote or a book by Ian Stewart. We teach rep theory out of a book by Martin Liebeck and Gordon James (If you are familiar with those texts).