This course presents mathematical foundations for learning, prediction, and decision making. Unlike in traditional statistical learning, however, our focus will be on notions of optimality that do not rely on stochastic modeling assumptions on data. A primary focus will be on learning from data to compete with a class of baselines predictors/strategies, often referred to as experts. A secondary focus will be on the ability to adapt to the presence or absence of statistical patterns, without presuming at the outset that such patterns will arise. Topics include: regret; prediction with expert advice; the role of the loss function in tight bounds; online classification; online linear and convex optimization; regularization; bandit problems/decisions with limited feedback; minimax optimality and adaptivity; relationships with statistical learning.