Inverse problems aim to solve the parameters given an observed or desired effect. These problems often lead to mathematical models that are inherently ill-posed in Hadamard’s sense. In many inverse problems, exact data are not available, instead, only noisy data are available. Hence, to obtain stable approximate solutions, regularization is used. In this course we introduce some basic mathematical background to study ill-posed linear inverse problems necessary to study the convergence of two classic regularization methods, Tikhonov regularization and the Landweber iteration.