This book presents a comprehensive and unifying introduction to kernel adaptive fi ltering. Adaptive signal processing theory has been built on three pillars: the linear model, the mean square cost, and the adaptive least - square learning algorithm. When nonlinear models are required, the simplicity of linear adaptive fi lters evaporates and a designer has to deal with function approximation, neural networks, local minima, regularization, and so on. Is this the only way to go beyond the linear solution? Perhaps there is an alternative, which is the focus of this book. The basic concept is to perform adaptive fi ltering in a linear space that is related nonlinearly to the original input space. If this is possible, then all three pillars and our intuition about linear models can still be of use, and we end up implementing nonlinear fi lters in the input space. -　　 This book presents a comprehensive and unifying introduction to kernel adaptive fi　ltering. Adaptive signal processing theory has been built on three pillars: the linear model, the mean square cost, and the adaptive least - square learning algorithm. When nonlinear models are required, the simplicity of linear adaptive fi　lters evaporates and a designer has to deal with function approximation, neural networks, local minima, regularization, and so on. Is this the only way to go beyond the linear solution? Perhaps there is an alternative, which is the focus of this book. The basic concept is to perform adaptive fi　ltering in a linear space that is related nonlinearly to the original input space. If this is possible, then all three pillars and our intuition about linear models can still be of use, and we end up implementing nonlinear fi　lters in the input space.