Good question... There is a impressive collection of books and online texts on the subject of neural networks (NN), but many of them are either very technical or focus on somewhat specific domains of application of the NN, artificial vision, pattern recognition and signal processing being the "natural" leaders in this genre.
I'd like to second Chaos' recommendation of
Fundamentals Of Neural Networks
Architectures, Algorithms And Applications
by Laurene Fausett
For an introduction to the field, this book strikes a good balance in terms of accessibility, detail and coverage. The alternative are older books circa 1995-2000 which tend to be a be more of the vulgarization type.
You can also wet your appetite with online resources such as:
Finally, at the risk of confusing you, at a time when you need a broad view on the subject, I'd like to plug a specific type of neural network: Numenta's Hierarchical Temporal Memory concept.