This course provides an introduction to modern techniques in the analysis of random structure in high dimensions, with an emphasis on applications in information theory, communications, statistics, random matrix theory, combinatorics, and learning. The course will cover a subset of the following topics, time permitting: Introduction and basic inequalities (Chernoff, Hoefding). The concentration-of-measure phenomenon. Variance bounds and the Efron-Stein inequality. Information inequalities. Logarithmic Sobolev inequalities. The Entropy method. Concentration and Isoperimetric inequalities. The Transportation method: Marton’s inequality, Talagrand’s inequality. Influence and threshold phenomena. Suprema of random processes.