These lectures will serve as an introduction to the quantum mechanics of classically chaotic systems, and provide the background needed for a good understanding of the lectures of the other speakers. The topics to be discussed include: Ergodic properties of classical dynamical systems; Classical statistical mechanics - transport phenomena, Green-Kubo formalism; Quantum systems and quantum statistical mechanics - Wigner and Husimi distribution functions, Green-Kubo formalism for quantum systems; The origins of "quantum chaos", Loschmidt echo; Ehrenfest and Heisenberg time scales; Energy level spacings - Random Matrix Theory (RMT) and associated ensembles; The B-G-S conjecture and approaches to a proof; Statistical properties of wave functions; Quantum ergodicity; Semi-classics; The Gutzwiller trace formula; Quantum statistical mechanics and transport theory, useful model systems, diffusive - ballistic crossover, localization, interactions with the environment, decoherence.