The book, just as the work of Mel Nathanson, to whom the contributions are dedicated, dealswith additive number theory. The volume provides the current snapshot of the state of the art in this field. For any reader, even for those starting at the advanced high school level ofmathematics, the book provides a broad introduction to the current state of the additive number theory. The field is enjoying quite a renaissance recently, judging by the number of publications and a number of Fields medals awarded to mathematicians in this field. Additive number theory has widely ranging applications in the real world in addition to many purely mathematical applications. Applications include, but are not limited to: communication theory and digital signal processing (like cell phone and other wireless applications), image processing,optimization, discrete geometry, etc.