[ramblenode]

The other suggestions in this thread are quite good. I'll add "Machine Learning" by Murphy. It's not strictly about neural networks but it's an ML classic and a rigorous introduction to the subject that will give you a principled understanding of the statistical fundamentals. For actual NN implementation the Karpathy and Nielson sources are excellent.

[p1esk]

Definitely not the starting point for someone who has no clue. Murphy is probably the very last thing one would read before becoming an expert, and start publishing ML papers.