Published at the end of the second century CE, the Mishnah is an edited record of the complex body of material known as oral Torah that was transmitted in the aftermath of the destruction of the Second Temple in 70 CE.
The Mishnah is not a code of Jewish law; it is a study book of law. Most passages in the Mishnah contain a dispute between different rabbinic sages.
The Mishnah consists of six orders (sedarim, singular seder סדר), each containing 7–12 tractates (masechtot, singular masechet מסכת; lit. "web"), 63 in total, and further subdivided into chapters [peraqim, singular pereq], and paragraphs [mishnayot, singular mishnah] or verses. The word Mishnah can also indicate a single paragraph or a verse of the work itself, i.e. the smallest unit of structure in the Mishnah. For this reason the whole work is sometimes called by the plural, Mishnayot.
Because of the division into six orders, the Mishnah is sometimes called 'Shas' (an acronym for Shisha Sedarim – the "six orders"), though that term is more often used for the Talmud as a whole.
The six orders are:
- Zeraim ("Seeds"), dealing with prayer and blessings, tithes and agricultural laws (11 tractates)
- Moed ("Festival"), pertaining to the laws of the Sabbath and the Festivals (12 tractates)
- Nashim ("Women"), concerning marriage and divorce, some forms of oaths and the laws of the nazirite (7 tractates)
- Nezikin ("Damages"), dealing with civil and criminal law, the functioning of the courts and oaths (10 tractates)
- Kodashim ("Holy things"), regarding sacrificial rites, the Temple, and the dietary laws (11 tractates) and
- Tohorot ("Purities"), pertaining to the laws of purity and impurity, including the impurity of the dead, the laws of food purity and bodily purity (12 tractates).
The Tosefta (which literally means “addition”) has traditionally been characterized as a text that provides explanation for murky sections of the Mishnah — its more dominant and well-studied counterpart. But not all scholars accept this theory, and a few fundamental questions about these two texts remain up for debate: Why were both texts necessary? Which really came first and what was the purpose of the second?
The Tosefta closely corresponds to the Mishnah, with the same divisions for sedarim ("orders") and masekhot ("tractates"). It is mainly written in Mishnaic Hebrew, with some Aramaic.
There is some debate whether the Tosefta was earlier than the Mishnah and perhaps as a type of proto-Mishnah. Some think there was a proto-Mishnah that formed the basis of both the Tosefta and the Mishnah. Other permutations are possible.
Whereas the Mishna was considered authoritative, the Tosefta was/is considered supplementary. Interestingly, the Talmud is said to often utilize the traditions found in the Tosefta to examine the text of the Mishnah.
Recent scholarship, such as that of Yaakov Elman, concludes that since the Tosefta, as we know it, must be dated linguistically as an example of Middle Hebrew 1, it was most likely compiled in early Amoraic times from oral transmission of baraitot [see below]. Professor Shamma Friedman has found that the Tosefta draws on relatively early Tannaitic source material and that parts of the Tosefta predate the Mishnah.
Alberdina Houtman and colleagues theorize that while the Mishnah was compiled in order to establish an authoritative text on halakhic tradition, a more conservative party opposed the exclusion of the rest of tradition and produced the Tosefta to avoid the impression that the written Mishnah was equivalent to the entire oral Torah. The original intention was that the two texts would be viewed on equal standing, but the succinctness of the Mishnah and the power and influence of Yehuda Ha-Nassi made it more popular among most students of tradition.
For more see http://www.jewishvirtuallibrary.org/tosefta
Midrash halacha - attempting to clarify or extend a law beyond the conditions assumed in the Hebrew Bible, and to make connections between then current practice and the biblical text. It made possible the creation and acceptance of new liturgies and rituals which de facto replaced sacrificial worship after the fall of the Second Temple: the maintenance of continuity by linking those practices to the words of the Torah.
Midrash halacha from the two centuries following the fall of the Temple was collected in three books — the Mekhilta on Exodus, the Sifra [book] on Leviticus, and the Sifrei [books] on Numbers and Deuteronomy — collectively known as the tannaitic midrashim.
Midrash aggadah - narrative midrash: interpreting biblical narrative, exploring questions of ethics or theology, or creating homilies & parables based on the texts. Most midrash aggadah were compiled between about 200 and 1000 C.E. (many midrashim circulated orally before then).
Baraita (Aramaic: ברייתא "external" or "outside"; pl. Barayata or Baraitot; also Baraitha, Beraita; Ashkenazi: Beraisa) is said to be a Babylonian terms designating a tradition in the Jewish oral law not incorporated in the Mishnah. "Baraita" thus refers to teachings "outside" of the six orders of the Mishnah. Originally, "Baraita" probably referred to teachings from schools outside the main Mishnaic-era academies – although in later collections, individual Baraitot are often said to be authored by or attributed to the sages of the Mishna (the Tanna'im).
According to Maimonides (Introduction to Mishna Torah), the baraitot were compiled by Rabbi Hoshaya and Bar Kappara, although no compilation was passed down as the Tosefta was.
These works are considered to have been the basic "proof-text" cross-referenced by the Talmudic sages in their analysis and interpretation of the Mishna; See Gemara. Here, a teaching from the Baraita is usually introduced by the Aramaic word "Tanya" ("It was orally taught") or by "Tanu Rabanan" ("Our Rabbis have orally taught"), whereas "Tnan" ("We have orally taught") introduces quotations from the Mishnah. Anonymous Baraitot are often attributed to particular Tanna'im by the Talmud. In the Jerusalem Talmud, references to Baraitot are less common.
The style of the Baraita is basically indistinguishable from that of the Mishna, but some come closer to Mishnaic idiom than others. For example, the second chapter of Kallah Rabbathi, a beraita compilation, is often appended to Pirkei Avoth, as both are similar in style and content.
For a more detailed explanation of the origins of the Baraita (in relation to the rest of the Mishna), see http://www.sacred-texts.com/jud/t01/t0106.htm