Artificial Neural Networks are quite useful and not realty complicated.
Here is a good example with programming code. The other chapter the same book are also very interesting.
http://natureofcode.com/book/chapter-10-neural-networks/
Anther simple example in Python
http://iamtrask.github.io/2015/07/12/basic-python-network/
And article about using ANN in Intrusion Detection Systems.
http://arxiv.org/pdf/1009.2406.pdf
Artificial Neural Network