1175. After two or more men have studied any amount of Torah Sheba'al Peh (e.g. Mishna, or Gemara) one may say Kaddish D'Rabbonon as long as there is a minyan present. Before beginning the Kaddish one should first say a "Dvar Aggadah" such as "Rebbi Chananaya ben Akashya etc." or "A'mar Rebbi Elazar A'mar Rebbi Chaninah Talmidei Chachomim etc." Shulchan Aruch w/Mishnah Berurah 54:3 MB9

1176. Kaddish may only be said when there is a minyan of ten Jewish males over Bar Mitzvah age. Women and children may not be counted towards the minyan. Shulchan Aruch w/Mishnah Berurah 55:1

1177. A minyan ten males is also required for Kedusha, Borchu, and Chazoras Hashatz. Shulchan Aruch w/Mishnah Berurah 55:1

1178. If one began saying Kaddish, (or Kedusha, Chazoras Hashatz, Nesias Kapayim, Krias Hatorah, or Haftorah) with the requisite minyan of ten, and then one or more of the ten left, one may complete the Kaddish (or the other above mentioned mitzvos) as long as there are at least six men remaining. Shulchan Aruch w/Mishnah Berurah 55:2

1179. If the Kaddish was the one immediately preceding Borchu, one may even continue to say the Borchu with the remaining six men since the Borchu is considered to be connected to the Kaddish that was started properly with a complete minyan of ten. Shulchan Aruch w/Mishnah Berurah 55:2

1180. If one was one of the ten needed for the minyan one may not leave and break the minyan, and one who does leave has sinned, because he has caused the Shechina to leave as the minyan was broken. [Thus, if one was asked to be a tenth to begin Chazoras Hashatz he is required to remain for the entire Chzoras Hashatz, until after the Kaddish after Shmona Esrei]. Shulchan Aruch w/Mishnah Berurah 55:2

1181. However, if there will still be a minyan of at least ten left without him, and one has already heard Kedusha and all the Kaddeishim until the end of davening one is permitted to leave the minyan. Shulchan Aruch w/Mishnah Berurah 55:2

1182. One should not leave the minyan at which he is davening until after the last kaddish at the end of davening has been completed. Shulchan Aruch w/Mishnah Berurah 55:2,

Piskei Tshuvos 55:7

1183. Jews who sin out of a lack of knowledge of the mitzvos (aka 'tinok shenishba') [even if they sin in a mitzvah that the Torah prescribes the death penalty for] may nevertheless be counted towards a minyan. Shulchan Aruch w/Mishnah Berurah 55:11

1184. One may not count someone who serves Avodah Zorah, or is Mechallel Shabbos openly in public towards a minyan. Shulchan Aruch w/Mishnah Berurah 55:11

1185. A Jew who sins purposefully as a rebellious act against Hashem, even in a single Mitzvah of the 613 mitzvos, may not be counted towards a minyan. Shulchan Aruch w/Mishnah Berurah 55:11

1186. One may not count one who denies the truth of Torah Sh'baal Peh - aka The Oral Torah (and certainly one who denies The Wriiten Torah received at Sinai via Moshe Rabbeinu) towards a minyan. Shulchan Aruch w/Mishnah Berurah 55:11, Piskei Tshuvos 55:21

1187. One should also not answer Amein to a Kaddish made by any of these people, even at a burial. Piskei Tshuvos 55:21

1188. If one [or even up to 4] of the minyan is/are davening Shmona Esrei and therefore unable to answer to the Chazzan's Kaddish [or Kedusha, Chazoras Hashatz, Nesias Kapayim, Krias Hatorah, or Haftorah], nevertheless he is [they are] counted as part of the minyan and the Chazzan may begin and/or continue, as the case may be. Shulchan Aruch w/Mishnah Berurah 55:6

1189. However, in Hilchos Tefillah the Shulchan Aruch appears to contradict this, by saying that regarding Chazoras Hashatz "if there are not nine being Mechaven (concentrating) to his berachos his berachos are close to being invalid". Shulchan Aruch w/Mishnah Berurah124:4

There are several resolutions to this apparent contradiction offered by the Poskim which we will address in coming halachos.

1190. According to the Perisha and Taz (we can resolve the contradiction between SA 55:6 and SA 124:4 mentioned in 1188 and 1189), L'chatchila one should not start Kaddish [or Kedusha, Chazoras Hashatz, Nesias Kapayim, Krias Hatorah, or Haftorah] unless there are 9 people to answer. However Bidieved, one may start as long as there are 6 who can answer. Perisha 124, Derisha 1, Taz 124:4, Birkei Yosef 55:6

1191. According to the Magen Avraham, the Maharil, the Elya Rabbah and others, the words of the Shulchan Aruch in 124 stating that 9 are necessary, is not the final ruling. Rather, the halacha follows the words of the Shulchan Aruch in 55 where he states that even if 1 [or up to four] are not able answer, they may still be counted towards the minyan, and the Chazzan may begin. Magen Avraham 55:8, Maharil 150, Piskei Tshuvos 55:11

1192. According to the Shulchan Aruch Harav and the Pri Megadim the Shulchan Aruch in Siman 124 is discussing only Chazoras Hashatz, and it is specifically there that 9 who can answer are required. In Siman 55 where the Shulchan Aruch says that one [or up to 4] may not be able to answer and the Chazzan may nevertheless begin, he is discussing Kaddish [or Borchu], but not Chazoras Hashatz. Shulchan Aruch Harav 55:7, see also Biur Halacha 55:6, Kitzur SA 20:2, Kaf Hachaim 48

1193. One who is beginning his own silent Shomona Esrei with the Chazzan's Chazoras Hashatz is counted towards the required 9 [or 6 Bidieved] people necessary for the Chazzan to begin Chazoras Hashatz. Mikvah Yisroel citing R' Shloma Zalman Auerbach 124:9, Piskei Tshuvos 55:11

1194. The generally accepted minhag is that at Maariv the Chazzan may L'chatchila begin Kaddish after Shmona Esrei as long as there are 6 in the minyan who are answering the Kaddish.

1195. However, for Chazoras Hashatz the accepted minhag is to L'chatchila wait until there are 9 people who can answer the berachos. However, in the event of great need (B'shaas Had'chak), if the minyan may break apart because one or more are davening very long Shmona Esrei's, or the long delay is a Tircha D'Tzibbura (a bother and discomfort for the tzibbur) then it is permitted for the Chazzan to begin Chazoras Hashatz with only 6 [i.e. the chazzan plus 5]. S'U Kinyan Hatorah 7:9, S'U Tzitz Eliezer 12:9, S'U Mishnas Yosef 5:17, S'U Mishna Halachos 4:9, Piskei Tshuvos 55:11

1196. One who was placed in Cherem (excommunication) by a Bais Din (a Jewish court) may not be counted towards a minyan, unless the cherem was regarding a financial matter, in which case he may be counted towards a minyan [unless the cherem specifically stated that he may not be counted towards a minyan]. Shulchan Aruch w/Mishnah Berurah 55:12, see Biur Halacha and Be'er Haitaiv

1197. In any event, one who was placed in cherem is permitted to daven in any shul, unless the cherem specifically stated that he is to be barred from davening in a shul. Shulchan Aruch w/Mishnah Berurah 55:12, see Biur Halacha and Be'er Haitaiv

1199. However, the The Chazon Ish rules stringently; that one must answer to Kaddish or Kedusha being said in another room/building, unless one is in middle of davening or learning and will be disturbed by having to respond. Ishei Yisroel 24:62, see also MB 56:MB6

1200. If one hears Kaddish, Kedusha or Borchu from a minyan in another room or building, and there is a gentile (who serves Avodah Zorah) between him and the minyan, one should not L'chatchila answer because the presence of the gentile is a separation between him and the presence of the Shechina at the minyan. Shulchan Aruch w/Mishna Berurah 55:20, Piskei Tshuvos 55:30

1201. A minyan should not L'chatchila daven Kaddish, Kedusha, Borchu or Shmona Esrei if a gentile(who serves Avodah Zorah) is standing amongst them. Magen Avraham 79:3, Piskei Tshuvos 55:30

Hilchos Borchu

1202. [When the chazzan says Borchu and] when responding to Borchu one should bow slightly towards Mizrach, but straighten out before saying Hashem's name. Biur Halacha 113:3, Aruch Hashulchan 57:1, Shulchan Hatohor 57:1, Shaarei Tshuva 57:1, Piskei Tshuvos 57:2

1203. However, many have the minhag not to bow at all, which is Minhag Ha'gra, while many Sefardim have the minhag that only the Chazzan bows, but not the Tzibbur. Nevertheless, one who is davening with a Tzibbur that bows, should also bow, and not change from the Minhag of the place. Shulchan Hatohor 57:1, S'U Or L'Tziyon 2:5:13, Shulchan Aruch Harav 109:2, Piskei Tshuvos 55:2 fn11

1204. One may complete Pesukei D'zimra after he has already said Borchu with the Tzibbur and it is not considered a hefsek. Shulchan Aruch w/Mishnah Berurah 54:MB14

1205. However, one should L'chatchila have in mind while saying Borchu that he will continue Pesukei D'zimrah after Borchu. Halichos Shlomo 6:20, Piskei Tshuvos 57:6