I am currently taking a class on Groups and Rings. I have been reading a text called Topics in Field Theory by Gregory Karpilovsky in my free time. I started reading this book mainly to motivate my study of Group and Ring theory. Inspired by this text, I have been wondering:
What are the fundamental/indispensable texts for the working field theorist?
I'm aware the Karpilovsky wrote another text titled Field Theory: Classical Foundations and Multiplicative Groups, but just by reading the preface I can tell that this one is more advanced than Topics in Field Theory, since the author says that he presents some of recent progress made in Field Theory up to that point (1989). However, I don't know if this book is nowadays considered "outdated" in the sense that it does not contain any progress made after 1989.
Note: I do not plan on immediately picking any text you recommend. What I want to do is "select" a recommended text and work towards it, making sure that I have the necessary background to approach it.
