Here main topic of discussion is on Linear and non-linear wave propagation and it’s application. At first we discussed about some concept of quasi-linear hyperbolic PDE, conservation law and their analysis. Then we used all those things on shallow water theory. Application:- Traffic Flow, Flood waves in rivers, Chemical exchange process, Glaciers, Erosion, Dam break problem, Piston wave maker problem etc. Here I also discussed about some different types of shallow water waves
