This lecture covers the principles of regression and linear systems, focusing on the iterative methods for solving linear systems, such as the Conjugate Gradient method. It delves into the importance of preconditioning and the convergence properties of iterative solvers, emphasizing the role of symmetric and positive definite matrices. The lecture also discusses the application of these methods in solving overdetermined systems and the considerations for choosing appropriate parameters. Additionally, it explores the impact of different parameter choices on the convergence of iterative solvers.