This chapter presents the foundational models based on formal neurons, commonly known as artificial neural networks or Deep Learning. These models have been pivotal in the development of quantitative methods in Artificial Intelligence, and we take particular care to present them within their historical context. It explores the capabilities of feedforward networks with a single hidden layer, which can approximate any continuous function under certain conditions related to the activation function used. Central to the effective training of deep neural networks is the backpropagation algorithm, which enables efficient computation of gradients needed for weight updates. The chapter discusses the use of gradient descent methods, including stochastic gradient descent and its variants, as essential tools for minimizing the loss function and optimizing network performance. To address the risk of overfitting and promote robust generalization, the chapter examines regularization strategies such as dropout and early stopping. These techniques either constrain the learning process or modify the network architecture, thereby improving performance on unseen data. The discussion also highlights the intriguing generalization abilities of overparameterized neural networks, noting that, despite their complexity, these models often perform exceptionally well in practice. The chapter concludes by emphasizing the need for further theoretical research to fully explain the generalization phenomena observed in deep learning.