The second Beracha of Birkat Ha'mazon begins with the word "Nodeh," which means "We give thanks." This theme of thanksgiving appears as well towards the end of the Beracha, when we recite, "Ve'al Ha'kol…Anachnu Modim Lach" ("For everything…we give thanks to You"). The Gemara says that if one mentioned the concept of "Nodeh" at either the beginning or the end of the Beracha, his recitation is satisfactory, even if he does not mention it at both ends of the Beracha. If, however, one makes no mention of this theme at all in the second Beracha, then his recitation is considered "Meguneh" (disgraceful). Nevertheless, the Rambam writes that his Beracha is still valid, and he need not repeat Birkat Ha'mazon.

Another important component of this Beracha is the mention of "Berit Ve'Torah" – circumcision and the giving of the Torah. Since this Beracha, which was composed by Yehoshua, expresses primarily our gratitude for G-d's giving us the Land of Israel, we must make mention of circumcision and the Torah, through which we earned the Land of Israel. We mention Berit Mila (circumcision) first, before Torah, because the word "Berit" appears thirteen times in the section of Parashat Lech-Lecha (Bereishit chapter 17) dealing with circumcision, signifying the thirteen covenants G-d established with Avraham with regard to circumcision, whereas the formal acceptance of the Torah occurred only three times in Jewish history.

Our practice is to mention "Berit Ve'Torah" twice: "Berit Ve'Torah Chayim U'mazon"; "Ve'al Beritecha She'chatamta Bi'vsareinu Ve'al Toratecha She'limadetanu." The Shulchan Aruch writes that if one did not mention "Berit Ve'Torah" in this Beracha at all, he must repeat Birkat Ha'mazon. Therefore, it is advisable to always recite Birkat Ha'mazon from a written text, to ensure that one recites it properly.

Women are obviously not included in the Mitzva of circumcision, and are also exempt from the obligation of Torah study. Therefore, if a woman failed to mention "Berit Ve'Torah" in Birkat Ha'mazon, she does not repeat Birkat Ha'mazon. Nevertheless, the Shulchan Aruch writes that women should make a point of including "Berit Ve'Torah" in Birkat Ha'mazon, since, as mentioned earlier, this Beracha expresses gratitude for the Land of Israel, which was given to us in the merit of these two Mitzvot. Since women must also be grateful for the Land of Israel, they should make mention of these Mitzvot in the Beracha of Nodeh.

In this Beracha we also mention the Exodus from Egypt: "Ve'al She'hotzeitanu Mei'eretz Mitzrayim U'fditanu Mi'beit Avadim" – "and for Your having taken us from the land of Egypt and redeemed us from the house of bondage." May a convert, whose ancestors obviously were not enslaved in Egypt, recite this passage? Halacha says that a convert may recite the text as, "Ve'al She'hotzeita Et Am Yisrael…U'feditam…" – "and for Your having taken the Nation of Israel…and redeemed them." Nevertheless, if a convert recited the standard text, he has nevertheless fulfilled his obligation, since he is, after all, a member of the Jewish people, and in some sense his soul was redeemed together with rest of the Jewish nation.

Summary:
1) One must recite the theme of thanksgiving at both the beginning and end of the second Beracha of Birkat Ha'mazon ("Nodeh"; "Ve'al Hakol…Anachnu Modim"). If one neglected to mention this theme, his recitation is nevertheless valid.
2) If one made no mention of "Berit Ve'Torah" (circumcision and the giving of the Torah) at all in the second Beracha of Birkat Ha'mazon, he must repeat Birkat Ha'mazon.
3) Women must also include "Berit Ve'Torah" in Birkat Ha'mazon, but if they failed to do so, they need not repeat Birkat Ha'mazon.
4) A convert may change the text that speaks of the Exodus so that it speaks of the Jewish people, rather than his forefathers; nevertheless, if he recited the standard text, he has fulfilled his obligation of Birkat Ha'mazon.

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