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This book is a revised edition of my earlier book of the same title. The cur- rent edition adopts the structure of the earlier version but is much changed. The introduction now contains definitions of stability. Chapters 2 to 4 ex- plain stability and the energy method in more depth and new sections dealing with porous media are provided. Chapters 5 to 13 are revisions of those in the earlier edition. However, chapters 6 to 12 are substantially revised, brought completely up to date, and have much new material in. Throughout the book new results are provided which are not available elsewhere. Six new chapters, 14 - 19, are provided dealing with topics of current interest. These cover the topics of multi-component convection diffusion, convection in a compressible fluid, convection with temperature dependent viscosity and thermal conductivity, the subject of penetrative convection whereby part of the fluid layer can penetrate into another, nonlinear sta- bility in the oceans, and finally in chapter 19 practical methods for solving numerically the eigenvalue problems which arise are presented. The book presents convection studies in a variety of fluid and porous media contexts. It should be accessible to a wide audience and begins at an elementary level. Many new references are provided.