Galois Theory is an algebraic theory providing a powerful connection between fields and groups. Many complicated problems involving fields can be converted to (possibly) simpler problems involving groups.

Galois Theory, albeit being extremely beautiful (it answers some very elementary questions, which were all open problems until its arrival), is far from being wildly known (i.e. by non-mathematicians). One of the reasons for this, in my opinion, is that is it a vast subject and most books on the topic are filled with too many details and so are inadequate for a quick read.

I wrote this short article as an introduction to Galois Theory. It is not very easy to read, but as it is very short (only 4 pages), I believe mathematically oriented readers, without excessive mathematical background will be able to read it. I chose to write it as a Latex document, instead of simple HTML residing directly in my site, as it contains a lot of complex mathematical notations.

The article consists of only the first part of the introduction to the topic. I believe that perhaps two more parts (of about equal length) will be necessary to complete the introduction.

If you like this article, let me know (this will enhance the chances of me actually writing down the remaining parts). If anything is not clear – please ask.

Enjoy!