This is part of the first systematic study of the formation of non-compound nouns and adjectives in Old and Middle Irish. It is divided into three sections: I. primary stem-formations; II. derivation via suffixation; III. other derivation modes. The analysis is both synchronic (inner-Irish) and diachronic (Celtic, Indo-Germanic) throughout and presents new findings of interest not least for the historical study of the phonology and morphology of Irish. It also charts new avenues for the description of word-formation in a corpus language. The analysis is based on a corpus of several thousand words whose etymologies have been verified.