What is the study of inscriptions known as?

Epigraphy, the study of the written matter recorded on hard or durable material. The term is derived from the Classical Greek 'epigraphein' (“to write upon, incise”) and 'epigraphē' (“inscription”).

Because such media were exclusive or predominant in many of the earliest human civilizations, epigraphy is a prime tool in recovering much of the firsthand record of antiquity. It is thus an essential adjunct of the study of ancient peoples; it secures and delivers the primary data on which historical and philological disciplines alike depend for their understanding of the recorded past.

In a narrower sense, epigraphy is the study of such documents as remains of the written self-expression of early cultures and as communication media in their own right, attesting to the development of visible sign systems and the art of writing as such. Finally, in later periods including the present, in which perishable writing media predominate, epigraphy affords insights into the styles and purposes of monumental or otherwise exceptional techniques of written recording.