Books on Group Theory. I am looking for a book/note that has a good collection of advance results,theorems on finite group theory.
By advance, I mean theorems after Sylow,Lagranges(I am considering theorems of Sylow,Lagrange as basic which  are available in any text of group theory).

I think one of the best and most complete book I know on (especially finite) group theory is Antonio Machì's http://www.springer.com/us/book/9788847024205 (original language: italian), despite the word "Introduction" in the subtitle. 
The author is also the translator of Herstein's much more elementary $\textit{Algebra}$.
There are also many exercises and explained examples. Chapter $1$ is elementary, chapter 2 and 3 introduce also some interesting and often advanced techniques, and the remaining chapter are mostly advanced (i.e., you won't see those results in a basic six-months course along with Sylow and Lagrange).
