Halakhah for Berakhot 7:1
שְׁלשָׁה שֶׁאָכְלוּ כְאֶחָד, חַיָּבִין לְזַמֵּן. אָכַל דְּמַאי, וּמַעֲשֵׂר רִאשׁוֹן שֶׁנִּטְּלָה תְרוּמָתוֹ, וּמַעֲשֵׂר שֵׁנִי וְהֶקְדֵּשׁ שֶׁנִּפְדּוּ, וְהַשַּׁמָּשׁ שֶׁאָכַל כַּזַּיִת, וְהַכּוּתִי, מְזַמְּנִין עֲלֵיהֶם. אֲבָל אָכַל טֶבֶל, וּמַעֲשֵׂר רִאשׁוֹן שֶׁלֹּא נִטְּלָה תְרוּמָתוֹ, וּמַעֲשֵׂר שֵׁנִי וְהֶקְדֵּשׁ שֶׁלֹּא נִפְדּוּ, וְהַשַּׁמָּשׁ שֶׁאָכַל פָּחוֹת מִכַּזַּיִת, וְהַנָּכְרִי, אֵין מְזַמְּנִין עֲלֵיהֶם:
Three who ate together chayavin lezamen. [They must "group" (lehizdamen) together to bless in the plural: "Let us bless Him of whose fare we have eaten."] A zimun (such a group) is made (even) if one ate: demai, [The fruits of an am ha'aretz (an unlearned person) are called "demai," i.e., "da mai?" "What is this?" Tithed or untithed? For amei ha'aretz are suspect in respect to tithes. And the sages forbade eating of their fruits until they were tithed. But if one did eat of them without tithing, the blessing (grace) is, nonetheless, recited, and it is not considered "a mitzvah coming through a transgression" because most amei ha'aretz do tithe], and ma'aser rishon (the first tithe) whose terumah had been taken, [even though terumah gedolah ("the great terumah") had not been taken of it. To wit: a Levite preceded a Cohein and took his ma'aser in the stalks, before the Cohein had taken terumah gedolah. The Cohein was to have taken terumah gedolah, one-fiftieth, first, the Torah calling it "reshith" ("the first"). It emerges, then, that the terumah gedolah of the Cohein is found in this ma'aser — one fiftieth of it — aside from terumath ma'aser, it being incumbent upon the Levite to separate terumah from his ma'aser. Our Mishnah apprises us that the Levite need not separate terumah gedolah from it, it being written (Numbers 18:26): "Then you (the Levites) shall separate from it terumah for the L-rd, ma'aser from the ma'aser" — ma'aser from the ma'aser, and not terumah gedolah and terumath ma'aser of the ma'aser.], and ma'aser sheni (the second tithe) and hekdesh (devoted objects) which were redeemed, [as when he gave the principal, but not the fifth (the owners adding a fifth), the tanna apprising us that the (absence of) the fifth does not stand in the way (of the blessing).], and (a zimun is made with) the waiter who ate an olive-size. [for we would think that since the waiter had no fixed place, but comes and goes, a zimun is not made with him; we are, therefore, apprised otherwise. In all of these instances we are apprised that though they are similar to what is forbidden, they do not constitute "blessing coming through transgression."], and (with) a Cuthite [one of the sect of idolators that the king of Ashur brought from Cutha and from other lands and settled in the cities of Shomron. They became proselytes from fear of the lions which started to devour them, as explained in II Kings (17), and they observed the written Law, being more fastidious than the Jews themselves in the observance of every mitzvah that they kept. They were, therefore, trusted in respect to certain mitzvoth until they were found to have set up an image of a dove on the top of Mount Gerizim, which they served. From that time on they were regarded as absolute idolators in every respect, for which reason today a zimun is not made with a Cuthite.] But a zimun is not made if one ate tevel [Grain from which terumah and ma'aser were not taken is called "tevel," ("tav lo" - "It is not good"). And not only (it goes without saying) is a zimun not made over what is tevel according to Scripture, but even over what is tevel by rabbinical ordinance, such as grain grown in an unperforated flower pot.], and ma'aser rishon whose terumah had not been taken. ["Terumah" here is not terumath ma'aser, for that would be absolute tevel, but the instance referred to is one in which the Levite preceded the Cohein to the pile after it had been finished off and become subject to terumah according to the Torah, and took ma'aser rishon first. One-fiftieth of that is subject to the Cohein's terumah gedolah; and so long as the terumah gedolah has not been separated, even though the terumah of ma'aser has been separated, no zimun is made over it. (If the Levite had preceded the Cohein and taken his ma'aser in the stalks, before the finishing off of the pile, there would be no need of separating terumah gedolah, as explained above).], and ma'aser sheni and hekdesh which had not been redeemed [It need not be stated that (no zimun is made) if they had not been redeemed at all; for this goes without saying. The reference is, rather, to an instance in which it had been redeemed, but not according to the halachah, as when ma'aser sheni is redeemed with fragments of silver or with a coin which has no design on it, Scripture having stated (Deuteronomy 14:25): "Vetzarta the money" — money that has a tzura (design on it); and as when hekdesh is redeemed with land instead of with money, Scripture having stated (Leviticus 27:19): "Then he shall add one-fifth of the money."], and (with) the waiter who ate less than an olive-size. [This is a superfluous Mishnah; but since most (of the aforementioned instances) are repeated for a necessary teaching, this, too, is repeated.], and an idolator. [The reference is to a proselyte who underwent circumcision but not ritual immersion, the Mishnah apprising us that as long as he has not undergone ritual immersion he is still an idolator, not being considered a proselyte until he has undergone both circumcision and ritual immersion.]
Shulchan Arukh, Orach Chayim
The first blessing, Birkhat ha-Zan praises God for providing food for all His creatures. The second blessing, Birkhat ha-Areẓ, expresses Israel's special thanks for the good land God has given it. It speaks of the redemption from Egypt, the covenant of circumcision and the revelation of the Torah. The third benediction, Boneh Yerushalayim and also Neḥamah, consolation, asks God to have mercy on Israel and to restore the Temple and the Kingdom of David. These blessings also include a plea for God to always sustain and support Israel. This was the core of the Grace after Meals, but after the destruction of Bethar during the Bar Kokhba revolt in 135 C.E. a fourth blessing was added, Ha-tov ve-ha-metiv. It thanks God for His goodness praying that He may fulfill specific desires. This is followed by special petitions which begin with the word Ha-Raḥaman, "May the All-Merciful…" This part of the prayer was once for personal desires but it then became standardized. The number of petitions vary. The Sephardi rite has fifteen while the Ashkenazi only has nine.
The Talmud (Ber. 48b) ascribes the origin of each of the benedictions to different Jewish heros and events. The first was originated by Moses when he saw manna fall, the second by Joshua when he conquered Ereẓ Israel, the third by David and Solomon and the fourth by the rabbis at Jabneh although it might actually date back to as early as the reign of Hadrian.
The Birkhat ha-Mazon, on Sabbaths and festivals is usually preceded by Psalm 126, which reminds us of Zion and its restoration among our earthly delights. Whenever three or more men have eaten together one of the men begins the Grace by summoning the others, (Ber. 7:1-5), "Gentlemen, let us say Grace", (in the Sephardi rite it is "with your permission"), and the others reply "Blessed be the name of the Lord henceforth and forever." The leader repeats that statement and says, "With your consent (the Sephardim say, "With the permission of heaven"), let us now bless Him of whose food we have eaten." The others respond, Blessed be He whose food we have eaten and through whose goodness we live." This whole introduction is called zimmun (Ber. 45b). The Talmud states that this must be said also by three women who eat together. The zimmun becomes somewhat longer when the number of people together goes to ten, a hundred, a thousand, and ten thousand. Now we insert the word Elohenu, "Our God" in the third line when ten or more eat together. Grace used to be followed by a cup of wine and there was a discussion if this was only when the grace was said with zimmun or also individually, (Shulḥan Arukh, Oraḥ Ḥayyim, 182:1). The custom now is to have the wine only on Sabbaths, festivals, and special occasions.
On Sabbaths and festivals special sections are added to the third blessing, Boneh Yerushalayim, these are Reẓeḥ and/or Ya'aleh ve-Yavo and an additional petition is added in series of Ha-Raḥaman. Special Ha-Raḥaman petitions are inserted for New Moons, Rosh HaShanah, Sukkot, Passover, and Shavuot. On Ḥanukkah and Purim the special Al ha-Nissim, "about the Miracles", section is said during the second blessing which is devoted to the thanksgiving.
The Grace at a wedding feast is slightly different. The third line of the zimmun is supplemented by "Blessed he our God in whose abode is joy, of whose food we have eaten, and through whose goodness we live" and then the seven wedding benedictions are recited at the end of the Grace. The Grace at the house of a mourner is also changed. The end of the third benediction has a special prayer substituted, the text of the fourth blessing is changed as is the zimmun. At a circumcision ceremony, the wording of the zimmun changes to fit the occasion. The Ha-Raḥaman petitions also allow for passages to be inserted by children, guests or masters of the house.
The Birhat ha-Mazon is the only prayer commanded by the Torah but the words were developed by man. Therefore under certain circumstances and for children different, shorter versions have been developed which at least mention the land and Jerusalem. When bread is not eaten another form of Grace is said. It is called Berakhah Aḥronah, a "final benediction" and what is said depends on what is eaten. When one eats of food from the five species of grain; wheat barley, rye, oats, and spelt, wine, or fruits of Ereẓ Israel, a short Grace is said, which consists of one benediction with an insertion for the type of food eaten and for the special nature of the day if it is the Sabbath or a festival. It is called Berakhah Me'ein Shalosh, "a benediction summarizing the three" regular benedictions. For any other food a short benediction called Ve-Lo-Khelum, "nothing" is said. It is also known by its first two words, Bore Nafashot.
Editorial Staff, E. J., v. 7, pp. 838-41.) he has to mention Yom Kippur in “יעלה ויבא״138Ya'aleh ve-Yavo, יעלה ויבא, "May our Remembrance rise and come and be accepted before Thee" is a special insertion made to the third blessing of the Grace after the Meal, Birkhat ha-Mazon, (see footnote 137) called Boneh Yerushalayim, which speaks about the restoration of the Temple and the Kingdom of David. It also asks God to have mercy on Israel. The blessing includes a plea for God to sustain and support Israel. The insertion of the Ya'aleh ve-Yavo is made on the festivals and New Moons and the Reẓeh on the Sabbaths. Both are inserted when the Sabbath falls on a festival. Since Yom Kippur is a fast day, there is no special insertion which specifically mentions Yom Kippur in the Birkhat ha-Mazon which is the Grace after Meals, of which there are not to be any on Yom Kippur. According to the Shulḥan Arukh if one must eat on Yom Kippur for reasons of health and then is able to, he must recite the Grace after Meals, and in the third blessing, the Boneh Yerushalayim he must insert the Ya'aleh ve-Yavo prayer which states that it is indeed a holiday, and at the time in the prayer when the specialness of the festival is mentioned, the person must also say "Yom ha-Zikharon ha-Zeh, "This Day of Remembrance" which indicates it is Yom Kippur.” in his Grace after the meal, namely in the benediction called “בונה ירושלים139Boneh Yerushalayim, בונה ירושלים, the third blessing in the Grace after Meals; see footnotes 137 and 138.”