Peninei Halakha 7, HaRav Eliezer Melamed (edited)
There are four [common] versions of Kaddish:
1) Half-Kaddish. This is the essence of the Kaddish. It is called Half-Kaddish so as to distinguish it from other Kaddishim which contain further additions. In any section of prayer where a prolonged interruption is undesirable, Half-Kaddish is recited.
2) Kaddish-Titkabal, also called Kaddish Shalem (Full-Kaddish). The chazan recites this Kaddish after the conclusion of the Amidah. In it, before the addition of Kaddish Shalem, a request is added that our prayers be accepted.
3) Kaddish Yehei Shelama, This is recited after saying verses of Scripture, and contains an added request for peace and good life for us and for all Israel. We conclude, “Oseh shalom bimromav… v’imru Amen”. Since this Kaddish is usually recited by people who have lost a parent, it is also called Kaddish Yatom (Mourner’s Kaddish).
4) Kaddish d’Rabbanan. This Kaddish is recited after learning rabbinic teachings. Before the addition of Kaddish Shalem, we add a prayer in this Kaddish for those who learn Torah, that they should merit long and prosperous lives.
Responding Amen to these additions is not as important as responding to the main part of the Kaddish. Therefore, one may not interrupt the recital of Birkot Keriat Shema and Pesukei d’Zimrah in order to respond to them
יֵשׁ לְכַוֵּן בַּעֲנִיַּת הַקַּדִּישׁ: הַגָּה: וְלֹא יַפְסִיק בֵּין יְהֵא שְׁמֵיהּ רַבָּא מְבָרַךְ וְלַעֲנוֹת אוֹתוֹ בְּקוֹל רָם, וּלְהִשְׁתַּדֵּל לָרוּץ כְּדֵי לִשְׁמֹעַ קַדִּישׁ:
הַגָּה: וְיֵשׁ לַעֲמֹד כְּשֶׁעוֹנִין קַדִּישׁ וְכָל דָּבָר שֶׁבַּקְּדֻשָּׁה, וּמִי שֶׁבָּא לְבֵית הַכְּנֶסֶת וְשׁוֹמֵעַ הַקָּהָל עוֹנִין קַדִּישׁ, עוֹנֶה עִמָּהֶם, אַף עַל פִּי שֶׁלֹּא שָׁמַע שְׁלִיחַ צִבּוּר שֶׁאָמַר יִתְגַּדַּל
One should have concentration when answering to kaddish. One should answer loudly and run to hear kaddish.
One should stand when responding to kaddish and to all holy moments, and if someone enters a synagogue and hears them responding to kaddish, they should respond with them, even if they did not hear the hazan start the prayer.
כְּשֶׁשְּׁלִיחַ צִבּוּר אוֹמֵר יִתְבָּרַךְ כָּל הָעָם עוֹנִין אָמֵן, וְכֵן כְּשֶׁאוֹמֵר בְּרִיךְ הוּא, וְכֵן כְּשֶׁאוֹמֵר וְאִמְרוּ אָמֵן:
When the chazzan reaches yitbarach, berich hu, and ve'imru amen, everyone should answer amen.
הָעוֹנִים עַד לְעָלְמֵי עָלְמַיָּא בִּלְבַד טוֹעִים הֵם, כִּי אָסוּר לְהַפְרִיד בֵּין עָלְמַיָּא לְיִתְבָּרַךְ.
Those who answer (say amen) only until l'almay almayah are wrong, because it is forbidden from disrupt between almayah and yitbarach.
כְּשֶׁאוֹמֵר הַחַזָּן יִתְגַּדַּל כּוֹרֵעַ, וְכֵן בִּיהֵא שְׁמֵיהּ רַבָּא, וְכֵן בְּיִתְבָּרַךְ, וְכֵן בִּבְרִיךְ הוּא, וְכֵן בְּאָמֵן.
When the hazan says yitgadal, respond. Also at y'hay shmay rabah, and also at yitbarach, and also at berich hu, and also at amen.
After he is done saying kaddish, he should take 3 steps back and then say oseh shalom etc.
[Just like the Amidah, because it has a kedushah]
רבי חנניא בן עקשיא אומר וכו׳
...שאין אומרים קדיש על המשנה אלא על האגדה, דאמר מר ויהא שמיה רבא דאגדתא.
Rabbi Chananya ben Akashia says, etc.: ...We do not say Kaddish over mishnah but rather over aggadah (homiletical teachings). As the master said 'May His name be exalted' (y'hay shmay rabbah) of aggadah."
הקדיש הוא שבח גדול ונורא שתקנו אנשי כנסת הגדולה אחרי חורבן בית ראשון. והיא תפילה על חילול שמו יתברך מחורבן בית המקדש, וחורבן ארץ הקודש, ופיזור ישראל בארבע כנפות הארץ. ואנו מתפללים שיתגדל ויתקדש שמו יתברך, כמו שאמר הנביא: "והתגדלתי והתקדשתי, ונודעתי לעיני גוים רבים, וידעו כי אני ה'." ....
ומפני גודל מעלתו תיקנוהו בלשון ארמית, מפני שבבבל דיברו בלשון זה. ולכן כדי שכולם יבינו – תיקנו בלשון המדובר. ועוד יש טעמים כמוסים בזה.
The Kaddish is great and awesome praise that the Men of the Great Assembly fixed after the destruction of the First Temple. It is a prayer about the desecration of the Blessed Name from the destruction of the Sanctuary, the decimation of the Holy Land, and the dispersion of Israel to the 4 corners of the earth. We pray 'let the Blessed name be magnified and sanctified' as the prophet said: "I will make myself greater and more sanctified and be known to the nations, and they will know that I am Hashem." ....
And because of its elevated status, it was decreed that it [the Kaddish] would be recited in Aramaic, because in Babylonia they spoke this language. And thus, so that everyone would understand it, [the Kaddish] was established in the spoken tongue. And, additionally, there are hidden reasons for this.
למימרא דמברך עדיף ממאן דעני אמן והתניא ר' יוסי אומר גדול העונה אמן יותר מן המברך
The Gemara asks: Is that to say that one who recites a blessing is preferable to one who answers amen? However, it was taught in a baraita that Rabbi Yosei says: the one who answers amen is greater than the one who recites the blessing.
But if everything is deteriorating, why does the world continue to exist? By the sanctification that is said in the order, [sidrah] and by the response: Let His great name [y'hay shmay rabah] be blessed, etc., which is recited after the study of aggada. As it is stated: “A land of thick darkness, as darkness itself; a land of the shadow of death, without any order” (Job 10:22). Therefore, if there are orders of prayer and study, the land shall appear from amidst the darkness.
שאחד נעדר בלי בן וצוה לפני פטירתו שילמדו עשרה כל יום תוך י"ב חודש בביתו בשכרם ואחר הלימוד תאמר הבת קדיש ולא מיחו בידה חכמי הקהילה והפרנסים.
Someone passed away with no sons, and willed before passing that each day for twelve months, ten shall be paid to study in his house, and after the studies the daughter will recite Kaddish. The sages of the community and the aldermen did not protest.
Leon Wieseltier, Kaddish, p115
The kedushah that is prescribed for the souls of the dead is known as the kedushah d’sidra, or the “kedushah of the lesson.” It was formulated in the academies of Babylonia in the geonic period, to be said after the verses from the Prophets that followed the conclusion of the morning study…thus the kedushah d’sidra…was strikingly similar to the kaddish d’rabbanan…which was the original version of the kaddish that was eventually adapted to the needs of the mourner…so perhaps this kedushah was a variety of the mourner’s kaddish. It was, you might say, the mourner’s kedushah.”
ואחר כך אומרים "ובא לציון גואל" כדרך שאמר ישעיה הנביא (נט יט): "כי יבוא כנהר צר, ובא לציון גואל". וגם אנחנו אחר "יענך ביום צרה" אומרים "ובא לציון גואל". ואחר כך אומרים פסוק "ואני זאת בריתי...", שגם ישעיה אמרוֹ אחר פסוק ד"ובא לציון גואל". כלומר: שלא תפחד שמרוב הצרות תשתכח תורה מישראל. לא כן, ד"לא ימושו מפיך...". וזה ראינו בחוש, שאחר חורבן בית המקדש שהרומיים גזרו עלינו גזירות קשות ורעות, ואז אדרבא נתחזקה התורה בזמן התנאים והאמוראים...
And afterwards say U'va L'tziyon, as Isaiah the prophet said: "For he shall come as a narrow river, and come to Zion as a redeemer." (U'va L'Tziyon) And we will also "answer on the day of trouble," saying, "and come to Zion as a redeemer." And after that we say the verse, "And I am my covenant," that Isaiah also said after the verse "U'va L'Tziyon". As it is said: That you should not be afraid during the great tragedies that you will forget the Torah from Israel. In fact, "They will not be exhausted from your mouth..." And we saw, in a sense, that after the destruction of the Temple that even though the Romans decreed terrible and awful decrees upon us, Torah was strengthened in the time of the Tannaim and the Ammoraim.
ואחר כך אומרים "ואתה קדוש". וזהו "קדושה דסידרא" שאמרו בסוף סוטה, דמיום שחרב בית המקדש אין יום שאין בו קללה, וכל יום קללתו מרובה מחברו....
ופירש רש"י: סדר קדושה שתיקנו שיהו כל ישראל עוסקין בתורה בדבר מועט, שאומר קריאתו ותרגומו, והן כעוסקין בתורה... ויש כאן קדושת השם ותלמוד תורה, וחביב הוא.
וכן "יהא שמיה רבה...". עד כאן לשונו.
And afterwards we say, "V'atah kadosh." That's "Kedusha d'Sidra." It's said at the end of Sotah that every day since the destruction of the temple there hasn't been a day without a curse, and every day the curse is worse than the day before....
According to Rashi, the order of the Kedusha was set so that all Israel was engaged in Torah (every day) in a small way - in its reading and its translation. They were involved in Torah... And here we have Kedushat HaShem and the study of Torah, and it is very dear.
The same is true for, "Y'hay shmay rabah" (May God's name be great).
Leon Wieseltier, Kaddish, p115
We say the [Kedushah D'Sidrah] at the departure of the Sabbath because the sinners of Israel are returning to Gehenna at that hour …and even if a man has been sentenced to the judgment of hell, hell is cooled for him if he was careful about the kedushah service during his lifetime. Therefore we say the kedushah as the Sabbath departs to save our own souls from Gehenna, and to provide some atonement for the sinners of Israel who are in hell, who will have at least a respite until the completion of this prayer.
(13th Century Pietists, based on Rabbi Akiva in the Talmud)
(This is also one explanation as to why we add extra prayers at the end of Shabbat - to extend it and give the dead more time in their respite)
הגה: וכשהבן מתפלל ומקדש ברבים פודה אביו ואמו מן הגיהנם
And when the son prays and sanctifies in public, he redeems his father and mother from Gehenom.
Yeshivat Har EtZion
ISRAEL KOSCHITZKY VIRTUAL BEIT MIDRASH (VBM)
According to Rashi, Kedusha De-sidra is, in essence, both an exercise in Torah study, through the Aramaic translation, as well as an opportunity to sanctify God's name. Similarly, Kaddish recited after studying aggadic passages also combines these two components: Torah study and kiddush Hashem.