Before moving to the actual adaptive filtering problem, we need to solve the optimum linear filtering problem (particularly, in the mean-square-error sense). We start by explaining the analogy between linear estimation and linear optimum filtering. We develop the principle of orthogonality, derive the Wiener-Hopf equation (whose solution lead to the optimum Wiener filter) and study the error surface. Finally, we applied the Wiener filter to the problem of linear prediction (forward and backward).