I would complement this bibliography with, the [deal.ii](http://www.dealii.org/) library. Probably, if you are interested in functional analysis, error estimates ecc., this is not the right place for you. If you want to have an essential, but rigorous, mathematical picture, plus implementation strategy and software, well, there in no better place check than [deal.ii tutorials](http://www.dealii.org/developer/doxygen/deal.II/Tutorial.html).

Let me also add that [Wolgangs's video lectures](http://www.math.tamu.edu/~bangerth/videos.html)  are a precious resource.