This chapter explores the optimization behind machine learning. Machine learning uses optimization to tune the parameters of a model to fit data, by minimizing the objective function. Fundamentally, this is an inverse problem solved with optimization. We begin with automatic differentiation and backpropagation, as they are the core algorithmic infrastructure needed to obtain gradients to optimize large-scale machine learning models. Automatic differentiation applies the chain rule to the computational graph of a function to compute its derivative with the same computational complexity and the same order accuracy as evaluating the function itself. This is the idea behind backpropagation in neural network training, although automatic differentiation is used more broadly in inverse problems and control. Next, we show how to train neural networks with optimization. This involves learning rate scheduling, batch normalization, hyperparameter optimization, and vanishing and exploding gradients. We also revisit reinforcement learning from the perspective of deep learning. Finally, we explore how to incorporate physics into machine learning algorithms using techniques from optimization.