The chazzan continues with Kaddish Tiskabbel, which serves as the conclusion of Mussaf. (We do not say Ein Ke’Elokenu or Aleinu at this point – Aleinu having been said before, in the Amida.)
Mincha: We immediately proceed with “Va’yehi binso’a ha’aron” and remove a Sefer Torah from the Ark. We call three aliyos (Kohen, Levi, Yisrael). It is traditional for the three aliyos to be sold, especially the last one, which serves as Maftir. We read in Parashas Acharei Mos (Vayikra 18:1‑30). The Maftir then reads the entire Book of Jonah (1:1‑4:11) for the Haftara. He concludes with Birkas HaTorah (we do not say “Al HaTorah” at Mincha).
We return the Sefer Torah to the Ark, the chazzan recites half‑Kaddish and all say the Shemoneh Esreh as found in the Machzor, adding the Viddui before “Elokai, netzor leshoni me’ra.”
In the chazzan’s repetition, Selichos and the confessional are added after Ya’aleh VeYavo. The chazzan then continues with Kedushas Hayom, etc., and at the conclusion he recites Avinu Malkenu (with the congregation), followed by Kaddish Tiskabbel.
Ne’ilah: We now begin the fifth and final prayer, the intense prayer that is the climax of Yom Kippur – Ne’ilah (lit. “closure”). We say Ashrei and U’va LeTziyyon, and the chazzan recites half‑Kaddish. Then all say the Ne’ilah Shemoneh Esreh as found in our Machzor, praying that every request for a good judgment be granted, and substitute every mention of “kesiva” (inscription) with “chasima” (sealing), concluding with an abbreviated confessional.
During the chazzan’s repetition we recite the 13 Middos numerous times, repeat the abbreviated confessional, and upon concluding we all say Avinu Malkenu.
The chazzan, and the congregation after him, says “Shema Yisrael” aloud. This is followed by “Baruch Shem Kevod Malchuso” aloud three times (by the chazzan and then the congregation) and finally “Hashem Hu HaElokim” aloud seven times by the chazzan and then the congregation.
The chazzan recites Kaddish Tiskabbel until “De’amiran be’alma Ve’imru Amen,” and the shofar is blown. Kaddish is then concluded.
Weekday Maariv: We add Ata Chonantanu. At the conclusion of Maariv, Kaddish Tiskabbel, Aleinu then Kaddish Yasom, LeDavid Hashem Ori, and Kaddish Yasom.
If the sky is clear, we recite Kiddush Levana.
Following Havdala at home and breaking our fast (fast ends in N.Y.C. at 7:33 E.D.T.), we start with the construction of the sukka.
Since Tachanun would not be said on most of the days of this month, we do not resume saying Tachanun until the 2nd day of Cheshvan.
The following chapters of Tehillim are being recited by many congregations and Yeshivos for our brothers and sisters in Eretz Yisrael: Chapter 83, 130, 142. –Y.K.