I have read sylow theorem from Contemporary abstract algebra by Joseph A Gallian. At first I could not understand the theorems, although after searching internet and getting some good pdfs I understood these theorems properly using group action. Although that did not completely cleared my concept. As after trying to solve number of nonisomorphic groups of given order I found out that I really could not solve it properly most of them. I once again searched internet but could not find any group articles that would clear up my concept. So it would be great if you can suggest me any books, article or anything that would clear up the doubts I have. Any help would be appreciated. Thanks.
Beachy-Blair: Abstract Algebra is a really good book in introductory abstract. algebgra
Robert B Ash: Basic Abstract algebra is also really good book.
I would suggest these two.