In the first part of the semester, we will consider solution methods for large linear systems. These problems arise, e.g., from the discretization of real-life problems and often exhibit sparse structures. We present and test different iterative solvers for such kind of systems.In the second part, we introduce the basic concept of error estimation and adaptivity within the context of the Finite Element (FE) method. \newline While the lecture focuses on the treatment of the required mathematical theory, the tutorial will place emphasis on the implementation of the developed schemes within the Matlab programming environment.