Midrash Tanhuma (Hebrew: מדרש תנחומא) is the name given to three different collections of Pentateuch aggadot; two are extant, while the third is known only through citations. These midrashim, although bearing the name of R. Tanḥuma, must not be regarded as having been written or edited by him. They were so named merely because they consist partly of homilies originating with him (this being indicated by the introductory formula "Thus began R. Tanḥuma" or "Thus preached R. Tanḥuma") and partly of homilies by aggadic teachers who followed the style of R. Tanḥuma. It is possible that R. Tanḥuma himself preserved his homilies, and that his collection was used by the editors of the midrash. The three collections were edited at different times; they will, therefore, be treated in chronological order.
Tanḥuma A, also called Tanchuma Buber, is the collection published by S. Buber (Wilna, 1885), who gathered the material from several manuscripts. Buber claimed that this collection, consisting of homilies on and aggadic interpretations of the weekly sections of the Pentateuch, was the oldest of the three, perhaps even the oldest compilation of its kind arranged as a running commentary on the Pentateuch, and he identified several passages which he saw as being quoted by Bereshit Rabbah. Buber postulated that this midrash (Tanḥuma) was edited in the 5th century, before the completion of the Babylonian Talmud. Buber cites a passage in the Babylonian Talmud that seems to indicate that the redactor of that work had referred to the Midrash Tanḥuma. Other scholars disagree, however, and do not see the Buber recension of Tanchuma as being older than the other versions. Townsend cites a section from Buber's recension which appears to be a quote from Rav Sherira's Sheiltot (8th century). (ed. Townsend, Midrash Tanchuma, xii)