This is the third of three chapters that aim to show how we can apply the knowledge introduced in previous chapters to formulate three widely used algorithms in the Data Science field. This chapter considers neural networks. Neural networks are a huge topic, and there are many textbooks dedicated to describing all the different types and giving the details of how they work. There are unsupervised and supervised neural networks dedicated to different tasks. We are only going to consider one type of supervised neural network: the single-layered and multilayered perceptrons trained using back-propagation of errors. Knowledge of this type of network is a good entry point to lots of other networks. This chapter introduces the basic idea of input data being passed through the network in a forward direction and the error being propagated backwards through the network with the network weights being updated using a gradient descent algorithm of the type described in Sect. 6.2.3 of Chap. 6 .