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|Mishnah and Neshamah:
The word Mishnah has the same letters as the Hebrew word Neshamah (soul). Studying Mishnah on behalf of the soul of the deceased can deliver the soul from harsh judgments and elevate it to a higher level in Gan Eden.
1. Learning Mishnayos in the Shiva home:
It is proper for the non-mourners to learn Mishanyos in the Shiva home throughout the Shiva. [Some are accustomed to have the Minyan learn Mishnayos between Mincha and Maariv in the Shiva home. Some study Mishnayos in correspondence to the Hebrew name of the deceased, as explained in Halacha 3. The Avel, however, may not participate in the learning being he is prohibited in Torah learning.]
It is a great merit for the soul of the deceased when others study Torah in its merit. For this reason, it is customary to divide the study of all the tractates of the Mishnah amongst friends and family, completing it by the Shloshim.
Whose name do you mention-the father or the mother: When learning Mishnayos in memory of the deceased, one is to mention the name of the father.
3. Learning Mishnayos according to the name of the deceased:
It is a widespread custom to study chapters of Mishnayos in accordance to the name of the deceased. One studies one chapter of Mishnayos per letter, choosing those chapters that begin with the letters of the name. For example, if the name is אברהם then one begins with a chapter that begins with an א and then continues with a chapter that begins with a ב and so on and so forth. In the event that there are two of the same letters in the name, one is nevertheless to study a full chapter for each letter. However, it is not necessary to study different chapters for each repeated letter, and one may repeat the study of the same chapter.
The name of the parent: When learning Mishnayos in accordance to the letters of the name of the deceased, one studies only in correspondence the name of the deceased and not the name of his parent.
See Chapter 18 Halacha 4L regarding Shiva and Chapter 25 Halacha 8 regarding the first year.
 Kitzur SHU”A 207:5; Aruch Hashulchan 378:8; See Nitei Gavriel 99:3; Pnei Baruch 10:35
 See Sefer Sukkas Shalom 1, brought in Nitei Gavriel 64, that learning Mishanyos in a group between Mincha and Maariv is the 6th and highest level of elevating the Neshamah
 Gesher Hachaim 20:4-1; Pnei Baruch ibid
 Sefer Ziv Hasheimos 29
 See Nitei Gavriel 64
 Igros Kodesh 17:271, printed in Shulchan Menachem 5:313
 Mishmeres Shalom Lamed 24; Igros Kodesh 17:271, printed in Shulchan Menachem 5:313; Nitei Gavriel 64:4
Other customs: Some are accustomed to also recite the chapters that correspond to the parent’s name. [Nitei Gavriel ibid]