Over the last few decades, there has been much research on reproducing kernel Hilbert space (RKHS) for machine learning. This monograph applies RKHS for nonlinear signal processing. It proposes a new statistical descriptor, called correntropy, to characterize the higher order statistical information and nonlinearity intrinsic to random processes. Correntropy and centered correntropy functions can be formulated as "generalized" correlation and covariance functions on nonlinearly transformed random signals via the data independent kernel functions. Those nonlinearly transformed signals appear on the sphere in the reproducing kernel Hilbert space induced by the kernel functions if isotropic kernel functions are used. The book offers new insights into the application of RKHS in nonlinear signal processing. Graduate students, professionals and researchers who are working on nonlinear signal processing and machine learning will find insightful information from the book.