The first one:  The book---"A first course in modular forms" by F. Diamond, J. Shurman is a good book to start to study classical modular forms.

The second one: The advanced one--- "Modular forms" by Toshitsune Miyake is also a very good textbook to learn modular forms. 

The more advanced books, you can consider to read the books by the Dr. Goro Shimura, who I think is the most professional mathematician in modular forms.

Good luck.