The formal semantic analysis of African languages is still a young subfield within theoretical linguistics. Starting with general overviews of the quantifier systems of individual African languages around two decades ago, there now exists a substantial body of fieldwork-based and autochthonous formal semantic research conducted by both African and non-African scholars. A major objective of these studies is to describe and analyse semantic phenomena in under-researched African languages. A second important aim is to examine the extent to which leading semantic theories—mostly developed on the basis of European languages—can be applied to non-European languages, and to determine what broader theoretical insights can be gained from formal semantic analyses of African languages. Research in this field has fostered the emergence of a new generation of African semanticists who will carry this enterprise forward. This is the first of two articles on formal semantics of African languages. The central aim of these articles is to provide scholars with a background in formal semantics with a general overview of semantic research activities focused on African languages. At the same time, the two articles will also be valuable to readers with a broader interest in African languages, offering them a range of empirical and theoretical questions as well as diagnostic tools to begin their own semantic investigations in the languages of their choice. This first article begins with a brief historical sketch of semantic research on African languages and then introduces formal-semantic approaches to interpretive phenomena associated with the nominal domain (NP, DP), such as definiteness, indefiniteness, universal quantification, and number.