The present thesis addresses the problem of how New Testament scholarship may best discern and eventually reconstruct the Aramaic backgrounds to the New Testament on linguistic grounds. The major works of the twentieth and twenty-first centuries are critiqued. The problems found with previous approaches highlight the need for future studies to be validated against the conclusions of a multitude of corollary disciplines. These include the morphology and syntax of the three major languages used in Judaea during the first-century CE and the translation techniques used to convey sources from one language in one of the other two. The most critical need demonstrated is that of a systematically developed awareness of first-century Judaean literary Aramaic. The best representative corpus of this dialect is that from Qumran. Therefore, the second part of the present thesis contains a systematically developed and paleographically verified grammar of Qumran Aramaic. This treatment summarizes the heterogeneity of Qumran Aramaic orthography, phonology, morphology, and syntax. A complementary chrestomathy and a collection of thirty-five plates of previously unpublished photographs of the Genesis Apocryphon are included in appendices.