It is known that ReLU neural networks provide continuous and piecewise linear (CPWL) mappings. In other words, the input domain can be partitioned into regions on which the neural network is an affine function. The number of these so-called linear regions is therefore a metric for the complexity of the network. In this project, we want to understand how linear regions of CPWL functions are modified through simple operations (e.g. addition, composition, max, ...). In particular, we propose to analyse in-depth the statistics of the number of linear regions of the composition of CPWL functions in low dimensions. The project requires a good understanding on deep neural networks and solid programming skills.