The Tosafot or Tosafos (תוספות) are medieval commentaries on the Talmud. They are printed in most Talmud editions, on the outer margin of the page. The authors of these commentaries are known as Tosafists (“ba’ale ha-tosafot”.) The period of the Tosafot began after Rashi had written his commentary; the first tosafists were Rashi’s sons-in-law and grandsons.
The word tosafot literally means “additions”. The reason for the title is a matter of dispute.
Some scholars, e.g. Heinrich Graetz, think the glosses writings about Rashi’s commentary on the Talmud.
Other scholars, e.g. Isaac Hirsch Weiss, note that many tosafot have no reference to Rashi. In this view, tosafot are an extension and development of the Talmud. Just as the Gemara is a commentary on the Mishnah, the Tosafot are commentary on the gemara.
The Tosafist Oeuvre and Torah u-Madda, Ephraim Kanarfogel, The Torah U-Madda Journal, Vol. 2 (1990), pp. 51-60
Collected Essays: v. 1, Haym Soloveitchik, The Littman Library of Jewish Civilization