Basics of Discrete Volterra Series -- Introduction -- Basic Definitions -- Nonlinear Sampled-Data Systems -- Multidimensional Z Transform -- Discrete Volterra Series in the Z Domain -- Conditions for Convergence and Stability -- Matrix Representation for Multiple-Input and Multiple Output Systems -- Nonlinear Systems with Fading Memory -- Further Considerations on Fading Memory -- Approximation of the System Response by Volterra Series -- Discrete Volterra Series for Binary Signals -- Associated Expansions -- Other Approximations -- Nonlinear Echo Cancellation -- Introduction -- Adaptive Cancellers -- Nonlinear Echo Cancellation in Data Transmission -- Interleaved and Passband Nonlinear Transversal Filters.