Midrash halakha (הֲלָכָה) was the ancient Judaic rabbinic method of Torah study that expounded upon the traditionally received 613 Mitzvot (commandments) by identifying their sources in the Hebrew Bible, and by interpreting these passages as proofs of the laws' authenticity.
The term midrash halakha is also applied to the derivation of new laws, either by means of a correct interpretation of the obvious meaning of scriptural words themselves or by the application of certain hermeneutic rules.
The word midrash is rooted in the term drash, literally "seek," or "enquire," but practically meaning exposition. Midrash is then "that which has been expounded," or more simply, a work focused on rabbinic exposition (of the Torah or of Torah based laws and ethics). The word is applied only to compilations of Tannaic midrash or to the Tannaic exposition process.
However, the common term midrash used by itself has come to be a shorthand for the term midrash aggadah which, in contrast to midrash halakha, are non-legal tannaic expositions that are based on the Bible. Midrash halakha is not aggadic, sometimes resulting in confusion with the common shorthand meaning of midrash. Instead, the product of midrash halakha are legal works, primarily Mishnah and Beraisa.
The phrase "Midrash halakha" was first employed by Nachman Krochmal, the Talmudic expression being Midrash Torah = "investigation of the Torah". These interpretations were often regarded as corresponding to the real meaning of the scriptural texts; thus it was held that a correct elucidation of the Torah carried with it the proof of the halakha and the reason for its existence.
In the midrash halakha three divisions may be distinguished:
The midrash of the older halakha, that is, the midrash of the Soferim and the Tannaim of the first two generations;
The midrash of the younger halakha, or the midrash of the Tannaim of the three following generations;
The midrash of several younger Tannaim and of many Amoraim who did not interpret a biblical passage as an actual proof of the halakha, but merely as a suggestion or a support for it (zekher le-davar; asmakhta).