Recommendations for finite element textbook?

Question

I am looking for a nice book for learning the mathematical theory of finite element methods. The book should be accessible to students who are familiar with basic real analysis and Lebesgue theory, but perhaps less familiar with partial differential equations. Some topics that such a book might include would be: $L^p$ spaces, distribution theory, Sobolev spaces, Hilbert Spaces, etc, in a fair amount of detail.