In standard textbooks, fluid dynamics is often introduced as a near-equilibrium approximation to classical kinetic theory. Recent advances, both in theory for out-of-equilibrium quantum field theories and experimental data from high energy colliders, have taught us that the textbooks are wrong: fluid dynamics quantitatively applies in out-of-equilibrium, and highly quantum-mechanical, situations. In these lectures, I will discuss how modern out-of-equilibrium fluid dynamics is set up, how it relates to familiar microscopic approaches such as kinetic theory and gauge/gravity duality, and how and when it breaks down. If time allows, I'll also mention hydrodynamics result for high-energy nuclear collisions at the LHC as an application of this out-of-equilibrium fluid dynamics framework.
