The College of Science, Department of Mathematics, discussed a PhD. dissertation entitled "Linear Instability and Nonlinear Stability of Some Convection Problems in Complex Porous Medium Layers" by postgraduate student Sanaa Lafteh Khalaf. This dissertation aims to present a comprehensive stability analysis and an in-depth examination of thermal convection, solutal convection, reactive solutal convection, thermo-solutal convection, and double-diffusive convection in a horizontal porous layer saturated with an incompressible fluid, in a porous layer governed by the Darcy-Brinkman model, in a Brinkman porous layer, in dual-porosity media, in bidisperse porous medium convection, and in an incompressible Kelvin-Voigt fluid with uniform internal heating.