This book describes several tractable theories for fluid flow in porous media while the important mathematical questions about structural stability and spatial decay are addressed. Thermal convection and stability of other flows in porous media are covered and a chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed, and waves in an elastic body with voids are investigated. Acoustic waves in porous media are also analysed in some detail. A chapter is included on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathematical Sciences at Durham University, United Kingdom.