Midrash, Hebrew, “interpretation”, is a type of Jewish literature concerned with the interpretation of biblical texts. Perhaps the earliest attempts in midrash concerned the Passover, and Haggadah which includes the interpretation of Deuteronomy 26:5-8.
The aggadic midrashim seeks to derive a moral principle or theological concept from scriptures, while the halakhic midrashim aim to explain the complete meaning of a biblical law. The rabbis formulated various rules to deduce hidden or new meaning, and midrash was produced from the tannaaitic period until the 12th century AD.
The best known example is the collection Midrash Rabbah on the Pentateuch and five megillot. Tanhuma contains discussions on the weekly portion of the Torah which is read on the synagogue. The pesiktot contain midrashim for special Sabbaths and festivals. Collections of midrashic teachings include Derekh Eretz Rabbati, Derekh Eretz Zuta, and Tanna de-ve-Elyahu. Avot de-Rabbi Natan is an expansion of the tractate Avot.
And Pirke de-Rabbi Eliezer contains stories about biblical events. From the 12th century various anthologies of midrashim were compiled which drew from earlier sources; examples include the Yalkut Shimeoni, and the Midrash de-Gadol. A.G.H.
Bowker, John, The Oxford Dictionary of World Religions, New York, Oxford University Press, 1997, p. 640