The Mishnah is basic compilation of the Oral law of Judaism; it was written down around 200 CE. However there is another compilation of oral law from that time period which is nearly as authoritative; this is the Tosefta. Rashi (in his commentary on Talmud Sanhedrin 33a) writes that the Mishnah was redacted by Judah haNasi in consultation with members of the Academy, while the Tosefta was edited by Rabbis Hiyya and Oshaiah on their own, thus the Tosefta is less authoritative. In many ways the Tosefta acts as a supplement to the Mishna.
The word 'tosefta' means 'supplement'. The Tosefta' is a Halakhic work which corresponds in structure almost exactly to the Mishna, with the same divisions for sedarim (orders) and masekhot (tractates). It is mainly written in Mishnaic Hebrew, with a few Aramaic sentences.
Much of the tosefta is currently regarded as being written shortly after the Mishna was redacted, and seemed to act as a supplement to it. The text of most of Tosefta agrees nearly verbatim with the Mishna, and often varies only slightly. The Tosefta offers authors' names for laws that are anonymous in the Mishna; It also augments the Mishna with additional glosses and discussions. However, recent scholarship, especially by Professor Judith Hauptman reveals that the Tosefta draws on source material earlier than the later material in the Mishnah. It may well be that parts of the Tosefta predate the Mishnah.
The Tosefta as we have it today functions like a commentary on unquoted Mishnaic material; It offers additional haggadic and midrashic material, and it sometimes contradicts the Mishna in deciding Halakha (Jewish law), or in declaring in whose name a law was given.