Introduction.- Two Recent Catastrophic Tailing Dams Accidents.- Examples of Recent Catastrophic Hydro-Dam Accidents.- Historic Failures "Statistics".- What the Public Wants; Public Reactions.- Justifying the Need for new Approaches.- Let's start with some serious Don'ts!.- System Definition.- Hazard Identification.- Defining Probabilities of Events.- Dam Stability Failures.- Consequences.- Tolerance and Acceptability.- Risk Assessment for the Twenty-First...