## Colloquium Talk

Hyperbolic systems of conservation laws appear in many different areain Physics and has a history of more than 200 years. It became part of the morderntheory of analysis of PDES just 65 years ago. Now this theory is a well developedbranch of Analysis. Aim of this talk is to tell this story. The first part of thetalk is concerned with the Lax- Glimm theory of classical shocks and wellposednessof initial value problem. The second part is on initial boundary value problemfor systems and different formulation based on entropy inequalities and boundarylayers. We touch up on the recent work in the subject with Anupam Pal Chaudhuryand P.G.LeFloch