This book offers a systematic presentation of persymmetric adaptive detection, including detector derivations and the definition of key concepts, followed by detailed discussion relating to theoretical underpinnings, design methodology, design considerations, and techniques enabling its practical implementation. The received data for modern radar systems are usually multichannel, namely, vector-valued, or even matrix-valued. Multichannel signal detection in Gaussian backgrounds is a fundamental problem for radar applications. With an overarching focus on persymmetric adaptive detectors, this book presents the mathematical models and design principles necessary for analyzing the behavior of each kind of persymmetric adaptive detector. Building upon that, it also introduces new design approaches and techniques that will guide engineering students as well as radar engineers toward efficient detector solutions, especially in challenging sample-starved environments where training data are limited. This book will be of interest to students, scholars, and engineers in the field of signal processing. It will be especially useful for those who have a solid background in statistical signal processing, multivariate statistical analysis, matrix theory, and mathematical analysis.