This book presents the adaptive linear and non-linear algorithms for time-domain and frequency-domain equalisation in terms of bit rate maximisation which can be achieved in discrete multitone-based systems. The purpose of this book is to introduce the reader to the techniques, methods and algorithms which can be used to analyse, design and implement adaptive equalisers in DMT-based systems. Analysis of the behaviour of advanced adaptive algorithms discusses in general methods. The prerequisite of knowledge is a typical undergraduate mathematics background of differential equations, calculus and complex variables. This graduate-level book is invaluable for engineers, researchers, undergraduate and postgraduate involved with the design of advanced digital signal processing algorithms in communications systems.