In this chapter, derive a fast algorithm for solving Toeplitz systems of equations. The method is based on a recursive technique referred to as the Levinson–Durbin recursion (LDR), where the order of the system is successively increased until the desired order P is obtained. The approach is refined using the Burg algorithm and the accompanying lattice filter structure. The analysis leads to computationally efficient algorithms for evaluating the AR prediction coefficients and the forward and backward prediction error sequences. We also discuss efficient methods for computing the determinant and the inverse of a Toeplitz matrix as well as a technique for orthonormalising an AR process. The material in this chapter is in standard use in the signal processing community for dealing with autoregressive modelling.