The course will be an introduction to the Neural Networks, with a specific focus on their history, their successes / defeats and their current status from both a theoretical and application point of view. In the initial part, biological neural networks will be briefly observed; we will then go on to illustrate what are the basic components of a neural network and how they are integrated into the model. We will then move on to studying the learning process in its main variants (unsupervised / supervised, reinforced, etc.) and the most popular network strategies / topologies. Following we will see a gallery of network models (Jordan, Elman, Hopfield, Radial-Basis, etc.) and, if time allows, we will discuss current themes in NN design: transformers, logical neural networks, fast/slow thinking models.