Experiments on high-energy heavy-ion collisions reveal the formation and intriguing properties of the Quark-Gluon Plasma, a new phase of matter predicted by Quantum Chromodynamics (QCD). The phenomenological relevance of relativistic hydrodynamics and the very weak observed viscosity indicate the presence of a strongly-coupled plasma expanding and cooling during the reaction.

As a tool to relate these dynamical features to a microscopic gauge field theory at strong coupling, time-dependent realizations of the AdS/CFT correspondence provide a stimulating way to study these properties in a realistic kinematical configuration. Relating a Yang-Mills gauge field theory with four supersymmetries (which is a conformal field theory, CFT) with gravity in the Anti-de Sitter space in 5 dimensions (AdS$_5$), the AdS/CFT correspondence provides a useful "laboratory" for yet unknown strong coupling properties of QCD. Besides the interest of revealing new aspects of the AdS/CFT correspondence in a dynamical set-up, the application to plasma formation leads to striking theoretical properties which we will discuss in the lectures.

The tentative plan of the lectures follows:

1. The emergence of an (almost) perfect hydrodynamic fluid at late proper-times after the collision
2. The duality between an expanding 4-dimensional plasma and a moving black hole escaping in the 5 th dimension
3. The intimate and general link between conformal hydrodynamics and the Einstein equations in the AdS$_5$ bulk
4. The unique possibility of studying the far-for-equilibrium stage of a gauge field theory at early proper-times