Every person who begins to learn Gemara knows that when he or she opens a volume of Gemara he will find the text of the Gemara in the center of the page, surrounded by two commentaries, one on each margin of the page: On the right margin is the commentary of Rashi, and on the left the commentary of Tosafot. When he turns the page, the order is reversed: Tosafot on the right and Rashi on the left.
The Jewish child becomes acquainted with Rashi at an early age, when she or he starts learning Chumash with Rashi. But it may be several years later before he becomes acquainted with Tosafot, for when he begins learning Gemara, his study is limited to Rashi's commentary. Rashi is a continuous explanation of the text of the Gemara, which can be studied on a lower level, by beginners, and on a higher level by more advanced students. But Tosafot is more difficult, for it is a commentary on selected passages of the Gemara, or a commentary on Rashi's commentary, and it usually raises problems and questions, which often entail involved discussions.
Tosafot means "additions," being composed by Rashi's students and successors as "additions" to the commentary of the great master. They did not consider themselves as founders of a new and original school of interpreters of the Talmud, but rather as disciples of Rashi; they wished only to add and further clarify certain passages which their great master, in his desire for brevity and simplicity, had explained very briefly; or which Rashi, in his great wisdom and knowledge, saw very clearly, but which to lesser minds presented certain problems. But, as a matter of fact, the Tosafists (or Ba'alei haTosfos - "authors of Tosafot") introduced a new method of discussion of the Talmud, which compares similar talmudic discussion in different parts of the Talmud, pointing first to an apparent disagreement, and then proceeding to iron out the differences. Sometimes it leads the Tosafot to explain certain passages differently from Rashi. This gave rise to later Talmudic scholars to attempt to iron out the differences between Rashi and Tosafot, and thus the discussions of the Talmud went on, and still go on. But it can safely be said that one who is familiar with the Gemara together with Rashi and Tosafot commentaries is certainly a Talmudic scholar. Rashi passed away in the year 4865 (1105), and after his death began the era of the Tosafists which lasted for about 200 years. Rashi had written his commentaries on almost the entire Talmud, but on certain tractates (volumes) of the Talmud his commentary remained unfinished. Thus we find the following entry by his disciples in the middle of tractate Makkot (page 19b), where Rashi's commentary ends with a reference to purity of body (and soul): "Our master of pure body, his soul having expired in purity, commented no more. From here on, it is the language of his pupil Rabbi Yehuda bar Nathan." Rabbi Yehuda was Rashi's disciple and son-in-law. Similarly Rashi's commentary on Baba Batra was not completed, and it was completed by Rashi's grandson Rabbi Shmuel ben Meir.
Although both Rabbi Yehudah and Rabbi Shmuel received instruction from their father-in-law and grandfather respectively, and were great scholars and commentators in their own right, their commentaries, side by side with Rashi's, show that they had not reached Rashi's high level, which has remained unequaled.
Rashi had no sons; he only had three daughters, who were married to distinguished scholars. The oldest daughter was the wife of Rabbi Meir ben Shmuel, and they were the parents of three outstanding Tosafists: Rabbi Shmuel ben Meir (RaShBaM), already mentioned; Rabbi Yitzhak ben Meir (RIBaM), and Rabbenu Yaakov Tam, known as Rabbenu Tam. Rabbenu Tam was one of the most brilliant Tosafists. These three brothers had a sister, who had a son Rabbi Yitzchak, known to all students of Tosafot as the RI, who is the one most frequently quoted in the Tosafot. On his father's side, the RI was a grandson of Rabbi Simchah of Vitry, the famed author of Machzor Vitry, who was also one of the Tosafists.
Rashi's second son-in-law was the above named Rabbi Yehuda bar Nathan (RIBaN), who had a son Rabbi Yom Tov.
Rashi's third son-in-law was Rabbi Ephraim.
The Tosafists included the greatest Talmudic scholars who lived in France and Germany during the 12th and 13th centuries. Among them were Rabbi Yitzchak ben Asher haLevi (RIBA), a disciple of Rashi, Rabbi Shimson ben Abraham of Sens, Rabbi Yaakov of Orleans (who died a martyr's death in the riots against the Jews in London in the year 1189), Rabbi Yom Tov bar Yitzchak (who also died a martyr's death in the English city of York in 1190), and many others. Among the last of the Tosafists were such great luminaries as Rabbi Yechiel of Paris, Rabbi Meir ben Baruch of Rothenburg, and Rabbi Asher ben Yehiel, who moved to Toledo in Spain. These and other scholars transplanted the teachings of the Tosafists to other centers of Talmudic learning, which are still studied ardently in every Yeshiva throughout the Jewish world.