I watched one of the videos, titled "Galois groups, intuitively".[1] It is about 18 minutes long and gave me a somewhat understandable overview what Galois groups are (not the theory yet!).
I suppose if you have the time to spare, at least it should give you an idea if the topic is of interest and whether you need to remind yourself of some mathematical concepts to be able to study rest of the material, or if it is too elementary for you and a shorter treatise from elsewhere would be preferable.
(I actually thought I had learned something about Galois theory in University algebra, but either I hadn't, or I've forgotten more than I wanted to admit. Which is to say, if you watch the video, your mileage may vary!)
Someone could tell you that Galois theory is the study of field extensions and the structure of their automorphism groups but is that really going to help?
The fundamental theorem of Galois theory reduces certain problems in field theory (like finding roots of polynomials) to group theory (counting permutations and symmetries), which makes them simpler and easier to understand and solve (or prove non-solvable). Galois theory is the proof and applications of this theorem, and related topics. Key to this theory is being more methodical about extending the rational numbers into the real numbers, by introducing new numbers one at a time, instead of all at once.
One of the immediate discoveries in beginning this study is the fact that in many common cases you cannot add just one numbers one at a time, but must add 2 or more numbers at once. These sets of numbers are called conjugates, and have the interesting property that even though you can prove how many must exist and that they are distinct from each other, they are otherwise identical except in the arbitray names you give them.
