I have found a very useful book describing and explaining neural networks http://neuralnetworksanddeeplearning.com/index.html
As you may know, this technique is widely used for computer-learning applications, including optical character recognition and face recognition. I was vaguely aware of how they work from reading Steven Pinker's How the Mind Works
but this book goes into great detail and even provides software and a real example that you can experiment with on your own computer. Coincidentally, the example used to illustrate the technique is the recognition of handwritten digits, which we all have had some experience with.
There is a bit of mathematics in it but it is not too complicated if you have taken a linear algebra course, although I find he provides too much explanation in some parts and not enough in others. I have just got into the book so I will let you know later on if it is as good as it appears.
If you want to understand how computers will eventually put us all out of work, this is an important book. (He asks for only a $3 donation so perhaps he anticipates our imminent unemployment)