This publication was conceived as a textbook for a first-year graduate course in the Signals and Systems Area of the Electrical Engineering Department at UCLA to introduce basic statistical concepts of detection and estimation and their applications to engineering problems to students in communication, telecommunication, control, and signal processing. Students majoring in electromagnetics and antenna design often take this course as well. It is not the intention of this book to cover as many topics as possible, but to treat each topic with enough detail so a motivated student can duplicate independently some of the thinking processes of the originators of these concepts. Whenever possible, examples with some numerical values are provided to help the reader understand the theories and concepts. For most engineering students, overly formal and rigorous mathematical methods are probably neither appreciated nor desirable. However, in recent years, more advanced analytical tools have proved useful even in practical applications. For example, tools involving eigenvalue–eigenvector expansions for colored noise communication and radar detection; non-convex optimization methods for signal classification; non-quadratic estimation criteria for robust estimation; non-Gaussian statistics for fading channel modeling; and compressive sensing methodology for signal representation, are all introduced in the book.