This book provides an overview of radar waveform synthesis obtained as the result of computational optimization processes and covers the most challenging application fields. The book balances a practical point of view with a rigorous mathematical approach corroborated with a wealth of numerical study cases and some real experiments. Additionally, the book has a cross-disciplinary approach because it exploits cross-fertilization with the recent research and discoveries in optimization theory. The material of the book is organized into ten chapters, each one completed with a comprehensive list of references. The following topics are covered: recent advances of binary sequence designs and their applications; quadratic optimization for unimodular sequence synthesis and applications; a computational design of phase-only (possibly binary) sequences for radar systems; constrained radar code design for spectrally congested environments via quadratic optimization; robust transmit code and receive filter design for extended targets detection in clutter; optimizing radar transceiver for Doppler processing via non-convex programming; radar waveform design via the majorization-minimization framework; Lagrange programming neural network for radar waveform design; cognitive local ambiguity function shaping with spectral coexistence and experiments; and relative entropy based waveform design for MIMO radar. Targeted at an audience of radar engineers and researchers, this book provides thorough and up-to-date coverage of optimisation theory for radar waveform design.