Introduction to information theory -- Statistical physics and probability theory -- Introduction to combinatorial optimization -- A probabilistic toolbox -- The random energy model -- The random code ensemble -- Number partitioning -- Introduction to replica theory -- Factor graphs and graph ensembles -- Satisfiability -- Low-density parity-check codes -- Spin glasses -- Bridges : inference and the Monte Carlo method -- Belief propagation -- Decoding with belief propagation -- The assignment problem -- Ising models on random graphs -- Linear equations with Boolean variables -- The 1RSB cavity method -- Random K-satisfiability -- Glassy states in coding theory -- An ongoing story.