Of course, Galois and his fatal pistol duel were a long time ago, soooo, there are many polished presentations of Galois theory. E.g., in the abstract algebra

Of course, Galois and his fatal pistol duel were a long time ago, soooo, there are many polished presentations of Galois theory. E.g., in the abstract algebra text by I. N. Herstein can learn the basics of Galois theory in a few hours of study. Apparently the idea of using abstract algebra, especially fields (each of the rational, reals, and complex numbers are fields but not finite), for applications, especially to error correcting codes and, eventually, cryptography, date from Hamming back at Bell Labs. In college and grad school, I got dragged into finite fields and related topics over and over. I was too patient and tolerant: I just don't like that math. I DO like linear algebra, especially for its connections with Hilbert space, differential equations, the math used in Maxwell's equations, differential geometry, optimization, relativity theory, Markov processes, and more but somehow I just don't like cryptography and error correcting codes. Back in college one of my profs just observed and remarked that I'm an analyst and not an algebraist! So, this situation may help others here at HN: Some people like math analysis while mostly others like math abstract algebra! Still, just for Galois theory, if want to learn it, then can do that in a few hours!