In this course, students learn to master tools, algorithms, and core concepts related to inference from data, data analysis, and adaptation and learning theories. Emphasis is on the theoretical underpinnings and statistical limits of learning theory. In particular, the course covers topics related to optimal inference, estimation theory, regularization methods, proximal methods, online and batch methods, stochastic learning,  generalization and statistical learning theories, Bayes and naive classifiers, nearest-neighbor rules, self-organizing maps, decision trees, logistic regression, discriminant analysis, Perceptron, support vector machines, kernel methods, bagging, boosting, random forests, cross-validation, and principal component analysis. Project themes selected by students in consultation with instructor.