Self studying algebra book- Dummit foote or any other? I am self studying Abstract Algebra. At the beginning I picked Herstein's algebra book as my first introductory text but I wasn't able to solve half of the problems in the exercises so I decided to first go through an "easier" text and so I decided to study from J. Gallian's Contemporary Abstract Algebra .    
Now I have finished reading this book and have solved 80-90% of the exercises from it. I believe I understand all the basic concepts now and can solve most of the standard exercises. I am now looking for a more advanced text (to strengthen my concepts) that covers the same material and the one I can go through on my own with a good collection of problems.     
I have already checked out Herstein- and after understanding the theory well enough from Gallian and solving loads of problems from it, its problems do not scare me anymore.     
I am thinking of Dummit foote. What do you guys think about it? Is this book alone sufficient to suit my needs?     
Any other suggestions would be welcome.    
Also please don't suggest more than two books- not only it make me confused over which one to read first, it is not possible for me to go through 3-4 or more books as I have to revise and study other subjects too but maybe later I can check them out.
Edit: It would be great if someone could tell me what do they think about Hungerford's algebra and P.Cohn's Basic Algebra? Would they satisfy all the conditions I stated above like having a nice collection of problems and good for self study and not too elementary.
How do these two compare to Dummit foote?
 A: I think the book by Dummit & Foote is an excellent text and really suitable for the purpose you want to use it for.
What distinguishes the book by Dummit & Foote in my opinion from a lot of other text on abstract algebra is that the text is very complete, and almost all the important results are discussed and proved in the main text. This in contrast to a lot of other books that leave results and investigations of important concepts to the reader (as exercises).
Since you have an overview of the basic concepts of abstract algebra, it might be good to go to all the details now. This is very well possible with Dummit & Foote, and therefore I strongly recommend it.
A: Personally, I would recommend Aluffi's Algebra Chapter 0. It's a graduate text, but it's easy to read; I used it for my first algebra text and I was fine. It teaches you the material from a categorical point of view, which is very useful (and probably essential if you're planning on going into algebra or algebraic geometry). Dummit and Foote is good too, but I greatly prefer Aluffi.
