This book explores a number of new constructions of generators of shy sets (Mankiewicz generator, Preiss-Tiser generator, Baker generator, Kharazishvili generator, ordinary and standard Lebesgue measures, etc), which naturally generate classes of null sets playing an important role in studying the properties of a function space. It includes several interesting infinite-dimensional generalisations of some classical results (Cramer rule, Lioville theorem, etc) in terms of generators of shy sets.