The past two decades have witnessed the onset of a surge of research in optimization. This includes theoretical aspects, algorithmic developments such as generalizations of interior-point methods to a rich class of convex-optimization problems, and many new engineering applications. The development of general-purpose software tools as well as the insight generated by the underlying theory have contributed to the emergence of convex optimization as a major signal-processing tool; this has made a significant impact on numerous problems previously considered intractable. Given this success of convex optimization, many new applications are continuously flourishing. This book aims at providing the reader with a series of tutorials on a wide variety of convex-optimization applications in signal processing and communications, written by worldwide leading experts, and contributing to the diffusion of these new developments within the signalprocessing community. The topics included are automatic code generation for real-time solvers, graphical models for autoregressive processes, gradient-based algorithms for signal-recovery applications, semidefinite programming (SDP) relaxation with worstcase approximation performance, radar waveform design via SDP, blind non-negative source separation for image processing, modern sampling theory, robust broadband beamforming techniques, distributed multiagent optimization for networked systems, cognitive radio systems via game theory, and the variational-inequality approach for Nash-equilibrium solutions.