Power crisis is common in almost all the developing countries. The study of cause and possible solution for the problem are presented mathematically. One of the components in a non-conventional energy source of Inertial Fusion is mathematically modeled as Rayleigh-Taylor Instability (RTI). RTI is one of the common phenomenons at the interface when lighter fluid supports a heavier one. The study of linear and nonlinear instability in a poorly electrically conducting fluid is presented in six different situations. In each case parameter of interested is identified and its effect on the growth of the instability is presented. This book gives huge information to the young researchers about the surface instability and allied problems