Linear regression is the most commonly applied procedure in statistics. This fact alone underscores the importance of solving linear least squares problems quickly and reliably. In addition, iteratively reweighted least squares lies at the heart of a host of other optimization algorithms in statistics. The current chapter features four different methods for solving linear least squares problems: sweeping, Cholesky decomposition, the modified GramSchmidt procedure, and orthogonalization by Householder reflections. Later we take up solution by the singular value decomposition.