analysis about elliptic PDEs I want to study elliptic PDEs,but i have no knowlegde the analysis behind it, such as Arzelà–Ascoli theorem,sobolev embedding,campanato space,Rellich theorem,Poincare inequality...
Do you have some suggested books about it? 
 A: The best way to learn PDE by yourself, I would say buy Evans book, and read chapter 2,5,6. It contains everything you mentioned in your post and presented in a very nice way. It won't be a easy task to learn elliptic PDEs by your own, but if you meet problems or difficulties, you are welcome to post it here and we will do our best to help you. :)
A: I agree with JumpJump that the best way to learn is by experience! Try and pick up things like the Sobolev and Poincare inequalities as you go through the material. Lots of lecture notes and proofs are available online for these fundamentals, but you will learn an intuition for these inequalities and compactness results best when seeing them applied to the theory of elliptic PDE, in my opinion.
If you specifically want books, in addition to Evans the book by Adams and Fournier is good for Sobolev spaces, and for elliptic PDE the best is Gilbarg and Trudinger. Don't let yourself get too bogged down reading the computations from books. A good exercise is to read the book to see the example of, say, elliptic bootstrapping, done for the Laplacian and then to try yourself to run the argument for more general elliptic operators.
