Hydrodynamics is known to describe matter created in high energy heavy ion collisions well. Large deposition of energy by passing jets should create not only the sound waves, already discussed in literature, but also the shocks waves of finite amplitude. This paper is an introduction to relativistic shocks, which go through elementary energy and momentum continuity argument, to weak shocks treated in Navier-Stokes approximation, to out-of-equilibrium setting of AdS/CFT. While we have not yet found numerical solution to corresponding Einstein equations, we have found a variational approximation to the sum of their squares. Our general conclusion is that deviations from LS and NS hydrodynmical shock profiles are surprisingly small, even for strong shocks. We end with a list of open questions which the exact solution should be able to answer.

Current version 2 has changed the basic numerical example of the strong shock, to somewhat stronger one. More details are provided on gradient expansion, as well as on individual components of the Einstein tensor and the total sum of squares. Multiple misprints corrected, text improved: conclusions are unchanged