In this chapter, we're going to introduce the concept of Hebbian learning, based on the methods defined by the psychologist Donald Hebb. These theories immediately showed how a very simple biological law is able to describe the behavior of multiple neurons in achieving complex goals and was a pioneering strategy that linked the research activities in the fields of artificial intelligence and computational neurosciences.

In particular, we are going to discuss the following topics:

• The Hebb rule for a single neuron, which is a simple but biologically plausible behavioral law
• Some variants that have been introduced to overcome a few stability problems
• The final result achieved by a Hebbian neuron, which consists of computing the first principal component of the input dataset
• Two neural network models (Sanger's network and Rubner-Tavan's network) that can extract a generic number of principal components
• The concept of Self-Organizing Maps (SOMs) with a focus on the Kohonen Networks