This Halacha is an excerpt from our Sefer
One may cut nails during the three weeks, up until the week of Tisha B’av. However, during the week of Tisha B’av, one may not cut nails. [This refers to from the Motzei Shabbos prior to Tisha Beav, until Tisha Beav, after which it becomes permitted to cut nails. If Tisha Beav falls on Shabbos, then one is to avoid cutting nails throughout that entire week, starting from Motzei Shabbos, with exception to Erev Shabbos as explained next. If Tisha Beav falls on Sunday, then there is no week of Tisha Beav that year, and cutting nails is permitted throughout the entire three weeksCutting nails during the three weeks.]
Erev Shabbos: If Tisha B’av falls on Shabbos one may cut his nails [on Erev Shabbos] in honor of Shabbos. [However, some Poskim rule one may only do so if he is accustomed to cut his nails on every Erev Shabbos. If, however, Tisha B’av falls on Sunday, one may cut his nails on Erev Shabbos even if he does not do so weekly, as the week before is not considered the week of Tisha Beav.]
Need of a Mitzvah: It is permitted to cut nails for the need of a Mitzvah, such as for Tevila.
 Opinion in M”A 551:11 [although is unclear if he refers to all nine days or only week of Tisha Beav]; Taz 551:13; Elya Raba 551:7; Mateh Yehuda 551:12; Chayeh Adam 133:17; Kitzur SHU”A 122:5; Derech Hachaim 4; Ben Ish Chaiy Devarim 13; M”B 551:20; Kaf Hachaim 551:48
Other opinions: Some Poskim rule it is permitted to cut nails throughout the nine days, even during the week of Tisha B’av, as this is considered a private custom of Aveilus, in which we are more lenient during the public mourning of the Temple. [Conclusion of M”A 551:11; Noda Beyehuda Kama Y.D. 99] Other Poskim rule one may not cut nails throughout the three weeks. [Kneses Hagedola 551:41] This is not the accepted custom.
 So is implied from M”A ibid that according to his first, stringent, approach we consider that entire week as the week of Tishe Beav, when Tisha Beav falls on Shabbos, and it is only permitted to be done on Erev Shabbos. [See Michaber 551:4 and Halacha 17G for a dispute regarding the status of the week of Tisha Beav when Tisha Beav falls on Shabbos.]
 M”A ibid; Elya Raba ibid; Levushei Serud 551 on M”A ibid that so applies even according to Taz; Ben Ish Chaiy Devarim 13; M”B ibid; Kaf Hachaim ibid
 Elya Raba ibid; brought in Kaf Hachaim ibid
 M”A 551:11; P”M 551 A”A 11; Chayeh Adam 133:17; Kitzur SHU”A 122:5; Derech Hachaim 4; M”B ibid; Kaf Hachaim ibid