Developing fast algorithms for solving large-scale sparse linear systems obtained from the discretizations for partial differential equations (PDEs) is an important and challenging task in modeling porous media. This course aims to introduce multilevel methods for solving such linear systems and discuss special challenges such as scalability, heterogeneity, and anisotropy. We first introduce the multigrid method and its algebraic variants using the diffusion problem as an example. We then use the multigrid method as a building block to develop multilevel iterative methods for solving PDEs arising from different porous media applications. The lectures will be given by Assoc. Prof. Xiaozhe Hu from Tufts University.