I've been trying to read the following note:
On the page 5 - 6, there is a brief review on the Galois theory of local fields. I'm trying to understand the things there, e.g. unramified extension, tamely ramified extension (and so on) of the field $K$, where $K$ is a finite extension of $\mathbb{Q}_p$.
In this post, I'm trying to find a detailed textbook to read things related to that.
I've been reading Serre's classical book "local fields" these days, but haven't found explicit proofs of the facts in the note. (Although so many people cited this book for details.) If there are indeed things on such topics, I'm hoping someone to tell me where they are and what to read (or what to skip) to reach the results.
I have turned to several notes, namely
NOTE for the MSRI summer school: https://www.overleaf.com/project/5c376d9cdfdb5c4f7a7e0377 (Course webpage: http://wwwf.imperial.ac.uk/~buzzard/MSRI/)
and
NOTE for the Arizona Winter School 2013 http://wwwf.imperial.ac.uk/~tsg/Index_files/ArizonaWinterSchool2013.pdf (Course webpage: https://www.math.arizona.edu/~swc/aws/2013/index.html)
But neither of them contains details on such things.
Thank you for commenting and answering! :)