This course provides a general introduction to machine learning with a view towards applications in finance. The goal is to provide both a solid grounding in the mathematical foundations of machine learning as well as a conceptual map of the field and its relation to areas like statistics and optimization that are currently more familiar in finance. The emphasis is on mathematical understanding, not implementation or financial specifics. Sample topics include generalized linear models, loss functions and regularization, sparsity, support vector machines, kernelization, principal components analysis, clustering, and the EM algorithm. Distinctions between classes of methods, such as probabilistic vs. variational models, Bayesian vs. frequentist approaches, and convex vs. nonconvex models.