chapter 1. Introduction -- chapter 2. General formulation of the discontinuous Galerkin method -- chapter 3. Discontinuous Galerkin method for one-dimensional nonconservative equations -- chapter 4. One-dimensional conservation laws -- chapter 5. One-dimensional shallow water flow in nonrectangular channels -- chapter 6. Two-dimensional conservation laws -- chapter 7. Two-dimensional shallow water flow in channels with horizontal beds -- chapter 8. Two-dimensional shallow water flow in channels with bed variations -- chapter 9. Pollutant transport -- chapter 10. Concluding remarks.