Introduction -- Fundamental theory for chemical dissolution front instability problems in fluid-saturated porous media -- Effects of particle reactive surface areas on chemical dissolution front instability in fluid-saturated porous media -- Effects of mineral dissolution ratios on chemical-dissolution front instability in fluid-saturated porous media -- Effects of medium permeability anisotropy on chemical dissolution front instability in fluid-saturated porous media. This monograph provides state-of-the-art theoretical and computational findings from investigations on physical and chemical dissolution front instability problems in porous media, based on the author's own work. Although numerical results are provided to complement theoretical ones, the focus of this monograph is on the theoretical aspects of the topic, and those presented in this book are applicable to a wide range of scientific and engineering problems involving the instability of nonlinear dynamic systems. To appeal to a wider readership, common mathematical notations are used to derive the theoretical solutions. The book can be used either as a useful textbook for postgraduate students or as a valuable reference book for computational scientists, mathematicians, engineers and geoscientists.