Book excerpt: Prepositions and cases constitute a fruitful field of research for semantics. The historical development of their meaning can shed light on the relations among the semantic roles of participants and on the organization of conceptual space. Ancient Greek allows an in-depth study of such development. The book, based on a wide, diachronically ordered corpus, aims at providing a usage-based analysis of possible patterns of semantic extension, including the mapping of abstract domains onto the concrete domain of space. An analysis of the Greek data further highlights the interplay between specific spatial relations and the internal structure of the entities involved, and shows how case semantics may account for differences on the referential level, rather than merely express clause internal relations. The first chapter contains a typologically based discussion of semantic roles, which sets the language-specific analysis in a wider framework, showing its general relevance and applicability.