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The aim of this book is to investigate linear and nonlinear stability of mono-diffusive (pure thermal) or double-diffusive (thermo-solutal) convection in a porous medium with induced inclined gradients. In this chapter 1 has provided some key definitions, and discuss the underlying theory of stability and instability with respect to linear and nonlinear stability analyses inherent in understanding flows through porous media. Chapter 2 deals with the problem of pure thermal convection induced by inclined thermal gradients with an internal heat source. Chapters 3 and 4, the stability analysis is performed on the double-diffusive Hadley flow induced by both thermal and solutal gradients, when it is subjected to gravity variations. In Chapter 5, the double-diffusive Hadley-Prats flow with a concentration based heat source is investigated through linear and nonlinear stability analyses. In both cases, the resulting eigenvalue problems have been numerically integrated using a combination of Shooting and Runge-Kutta methods. In the last Chapter, a summary of the present work and some future directions are discussed.