This chapter defines the most important basic notions and concepts figuring in the analysis of the system of qualifications of states of affairs and their expression in language, as they are used in the book. It defines the semantic categories figuring in the domain of qualifications of states of affairs (often called TAM categories), often in a preliminary fashion as some of them are elaborated or modified in later chapters. It introduces the notion of a hierarchy present in the system of qualificational dimensions, accounting for their semantic scope properties – an analytical concept central in the book. It moreover discusses the notion of a ‘semantic paradigm,’ as a system of expressive devices for a single qualificational category in which each member has slightly different functional characteristics, and it motivates the correlated function-to-form approach adopted in the study for analyzing qualificational categories and their expressions. The chapter moreover does some groundwork for the theoretical issue of the position of the hierarchical system in cognition, arguing that it is conceptual, not linguistic, in nature.