A Neural Network in 11 lines of Python

This is an excellent tutorial on neural networks that does a good job of explaining not only how they work but why they work as well. The python code is very easy to follow.

There is code for a very simple example and a more advanced one.

https://iamtrask.github.io/2015/07/12/basic-python-network/

see also:

http://denson-data-science.blogspot.com/2015/09/neural-network-step-by-step.html