In this book the new topic of lineability and spaceability is explored following closely the generalized trend in mathematics to search for large algebraic structures composed of mathematical objects with special properties. A state-of-the-art introduction to this concept is provided along with the current direction of research and a discussion of open problems in the field as well as potential solutions. Lineability and spaceability have a remarkable influence on real and complex analysis, summability theory, and general functional analysis.