This book is primarily a presentation of nonlinear energy stability obtained in convection problems by means of an integral inequality technique that is referred to as the energy method. While its use was originally based on the kinetic energy of the fluid motion, subsequent work has introduced variations of the classical energy. The new functionals have much in common with the Lyapunov method in partial differential equations and standard terminology in the literature would now appear to be generalized energy methods. In this book, the author describes many of the new generalizations and explains why such a generalization was deemed necessary. Additionally, he explains the physical relevance of the problem and indicates the usefulness of an energy technique in this context.