Les Houches lectures on deep learning at large and infinite width

These lectures, presented at the 2022 Les Houches Summer School on Statistical Physics and Machine Learning, focus on the infinite-width limit and large-width regime of deep neural networks. Topics covered include the various statistical and dynamical properties of these networks. In particular, the lecturers discuss properties of random deep neural networks, connections between trained deep neural networks, linear models, kernels and Gaussian processes that arise in the infinite-width limit, and perturbative and non-perturbative treatments of large but finite-width networks, at initialization and after training.