Fundamentals of Non-relativistic Collisionless Shock Physics: I. The   Shock Problem
  The problem of collisionless shocks is posed as the problem of understanding how in a completely collisionless streaming high-temperature plasma shocks can develop at all, forming discontinuous transition layers of thickness much less than any collisional mean free path length. The history of shock research is briefly reviewed. It is expressed that collisionless shocks as a realistic possibility of a state of matter have been realized not earlier than roughly half a centruy ago. The basic properties of collisionless shocks are noted in preparing the theory of collisionless shocks and a classification of shocks is given in terms of their physical properties, which is developed in the following chapters. The structure of this chapter is as follows: 1. A cursory historical overview, describing the early history, gasdynamic shocks, the realisation of the existence of collisionless shocks and their investigation over three decades in theory and observation until the numerical simulation age, 2. Posing the shock problem as the question: When are shocks? 3. Types of collisionless shocks, describing electrostatic shocks, magnetized shocks, MHD shocks, shock evolutionarity and coplanarity, switch-on and switch-off shocks, 4. Criticality, describing the transition from subcritical dissipative to supercritical viscose shocks, 5. Remarks. 
R. A. Treumann and C. H. Jaroschek