In this thesis I investigate the syntax and semantics of tense-aspect stem participles in the Ṛgveda, focusing primarily on the data from the earlier books II–VII and IX, seeking to establish a comprehensive and coherent analysis of this category within the linguistic system of Ṛgvedic Sanskrit. In recent literature tense-aspect stem participles are usually treated as semantically equivalent to finite verbs wherever possible, but contradictorily where they differ from finite verbs their adjectival nature is emphasized. I argue that tense-aspect stem participles are a fundamentally verbal formation and can be treated as inflectional verb forms: they are adjectival verbs rather than verbal adjectives. At the same time, however, they constitute an independent sub-category of verb form which is not necessarily semantically dependent on corresponding finite stems. I examine the syntactic and semantic properties of tense-aspect stem participles both in relation to finite verbal forms and their wider syntactic context, formalizing the evidence in the framework of Lexical-Functional Grammar. Consequently I am able to categorize the syntactic and semantic deviations which many participles exhibit in comparison to finite verbal forms. I contend that many such forms cannot be treated synchronically (and sometimes diachronically) as participles, but form distinct synchronic categories. My analysis permits a considerably more refined definition of the category of tense-aspect stem participles, dependent on clear morphological, syntactic and semantic criteria, as opposed to the usual, purely morphological, definition. From a diachronic perspective I argue that the category of tense-aspect stem participles as found in the Ṛgveda more closely reflects an inherited Proto-Indo-European category of tense-aspect stem participles than is usually assumed. I also reconsider theoretical treatments of participial syntax and semantics, and develop a more precise typology of non-finite verb systems which adequately accounts for Sanskrit participles.