This text is intended for use by engineers and researchers working in phased array theory and technology. It also contains practical design data for antenna designers, radar and communications engineers and array designers and researchers, and should be suitable for use on university courses on antenna rays. This reference provides complete design details enabling systems engineers to size an array system with the minimum of additional information, and includes enough detailed description of analytic methods to enable researchers to assess the state of electromagnetics applicable to this technology. In-depth descriptions include patttern optimization, elements and architecture for arrays and gain, directivity and various effeciencies for generalized arrays.