This is a package for learning about neural networks through a simplified example. There are many other better packages for production use.
The chapters folder contains a walk through for how to build up a neural network, starting with a simple linear classifier.
The source for a simple neural network that can have a variable number of layers each with a variable number of neurons can be found in src.
There are examples using the code in src for classifying XOR and MNIST image data. There is also an html file for visualizing how a linear classifier adjusts to classify AND.
Andrew Ng's Coursera class
Andrey Kurenkov's Brief History of Neural Networks and Deep Learning Parts I, II, III, and IV