This book deals with the following open problems: The Lineability Problem for Functionals (Aron and Gurariy, 2004); The Nowhere Density Problem for Functionals (Enflo, 2005); The Minimum-Norm Problem for Translations (Aizpuru and Garcia-Pacheco, 2003); The Banach-Mazur Conjecture for Rotations (Banach and Mazur, 1932). The first problem is on the linear structure of the set of norm-attaining functionals on a Banach space (it also considers the linear structure of the set of non-norm-attaining functionals). The second problem is on the topological structure of the set of norm-attaining...