When three people eat bread together, they are required to recite the introductory Zimun before Birkat Ha'mazon. The concept of Zimun is that we prepare ourselves for the Misva of Birkat Ha'mazon. When it comes to other Misvot, we prepare for the Misva act by reciting a Beracha. For example, we recite a Beracha before putting on Tefillin, and we recite a Beracha before shaking the Lulab. The Misva of Birkat Ha'mazon, however, is itself a series of Berachot, and so we need something else to prepare us. We therefore conduct a Zimun to prepare ourselves for the Misva of Birkat Ha'mazon. Different customs exist as to the precise text of the Zimun. The accepted text (as practiced by Hacham Baruch Ben-Haim) is that of the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), according to which the leader begins by announcing, "Hab Lan Ve'nibrich Le'Malka Ela-ha Kadisha." The others then respond, "Shamayim." The leader declares at that point, "Bi'rshut Malka Ela-ha Kadisha," and the others again respond, "Shamayim." Then the leader proceeds with "Nebarech She'achalnu," and if ten people are reciting Birkat Ha'mazon together, he recites "Nebarech Elo-henu She'achalnu." On certain occasions, the leader makes certain additions after he announces, "Bi'rshut Malka Ela-ha Kadisha." On Shabbat, he adds, "U'bi'rshut Shabbat Malketa"; on Yom Tob, he adds, "U'bi'rshut Yoma Taba." On Sukkot, he adds the name of that day's Ushpizin. At a Sheba Berachot, the leader says, "Nebarech Elo-henu She'ha'simha Bi'm'ono…" Interestingly, the Yam Shel Shelomo (Rav Shlomo Luria, 1510-1574) considered instituting this addition also at a Siyum Masechet, but he ultimately changed his mind, and so this text is not recited at a Siyum. Summary: When three or more people ate bread together, they are required to recite the introductory Zimun before Birkat Ha'mazon. The proper text is as follows: Leader: "Hab Lan Ve'nibrich Le'Malka Ela-ha Kadisha." Others: "Shamayim." Leader: "Bi'rshut Malka Ela-ha Kadisha." Others: "Shamayim." Leader: "Nebarech She'achalnu…" Others: "Baruch She'achalnu…" If ten or more people recite the Zimun, the word "Elo-henu" is added after "Nebarech" and "Baruch."