I am studying Galois Theory, and I am interested in studying this subject. I like this subject because of some crazy constructions, existence-nonexistence and various other things which motivates us to think. I have read some random books from library but I am not getting enough anything except Definition , Theorem. Hence I request you all to suggest some book which promotes thinking as well
I like Milne's notes on Galois Theory (except for the excesively concise treatment of the separability degree) as a quick (but more or less complete) introduction. For a more complete book, I prefer Bourbaki, Algebra, chap.V (it is definition-theorem style, but it is very well written, easy to read, and you will learn much more than with most other books).
These are books I've read in the past $6$ months trying to find a solution to a quintic equation. I think they might be in descending order or interest to you. (The "examples" in the first reference are mostly exercises for you to complete.)
Classical Galois Theory, With Examples by Lisl Gaal
Beyond the Quartic Equation by R. Bruce King
Abstract algebra and solution by radicals by John E Maxfield
The Past Master Or Fifth Degree Illustrated by Malcolm C. Duncan