In this chapter, we shall consider the design of neural nets, which are collections of perceptrons, or nodes, where the outputs of one rank (or layer of nodes becomes the inputs to nodes at the next layer. The last layer of nodes produces the outputs of the entire neural net. The training of neural nets with many layers requires enormous numbers of training examples, but has proven to be an extremely powerful technique, referred to as deep learning, when it can be used.We also consider several specialized forms of neural nets that have proved useful for special kinds of data. These forms are characterized by requiring that certain sets of nodes in the network share the same weights. Since learning all the weights on all the inputs to all the nodes of the network is in general a hard and time-consuming task, these special forms of network greatly simplify the process of training the network to recognize the desired class or classes of inputs. We shall study convolutional neural networks (CNNs), which are specially designed to recognize classes of images. We shall also study recurrent neural networks (RNNs) and long short-term memory networks (LSTMs), which are designed to recognize classes of sequences, such as sentences (sequences of words).