Despite the thorough research into the theory of wavelets, say Luthy and colleagues, a number of questions remain, such as the MRA structure, the structure of the space of negative dilates, and the variety of resolution structures that may occur. Here they offer a comprehensive yet technically fairly elementary approach to these questions, presenting a multitude of new results, resolving some of the old questions, and providing new developments for some problems that remain open for the future. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)