Hi I struggled with Galois theory as a senior, and would like to improve my ability to jump in and out of the subject with a sort of big picture to details map. So as I see it, there are four things to be proficient at: Knowledge and understanding of: Theory, Particular examples, Relevant group theory General examples, and how they all relate. I conjecture that to feel comfortable in the subject at the undergraduate level, you have to cover these four bases. Now I will go into more detail about what I mean by these each of these four. By THEORY, I mean understand all the theorems and what they say, and given any question on the theory, be able to dig through the chain of arguments to answer questions about the inner working of the theory. Also be able to recognize which facts tend to be use for which parts of examples. By PARTICULAR EXAMPLES, I mean taking a specific polynomial, or a field extension, and finding the splitting field, or irreducible polynomial respectively, and understand the group structure and the structure of the field extension. By RELEVANT GROUP THEORY, I mean it would be nice if so late in an algebra course, they did not fly past all the facts they need from group theory, it would be nice to have a focused presentation of group theory and for those facts that are used over and over in computing galois groups at this level. By GENERAL EXAMPLES, I mean along the idea that at some point they go through the arguments for general quadratics, general cubics, and some of the facts can be used for general nth degree polynomials, like the notion of discriminant. So it is a project of mine right now to find good sources to get a better feel for Galois so that I will not feel so disoriented in the subject. I get stuck way too often on reading people's arguments in the subject, because for instance Artin has very abbreviated reasoning. Please let me know if you think I'm missing something in the big picture.