How many walls must a Sukkah have?
The letter of the law:[1] From the letter of the law, it suffices to have two full[2] walls with a third wall using the rule of Lavud and Tzuras Pesach. This means that one is not required to have a full third wall but rather can have a partial full wall, and following the rules of Lavud and Tzuras Pesach, it is considered a full third wall. The exact details of how this Lavud wall is accomplished will be explained in D.[3]
The custom: It is a Mitzvah Min Hamuvchar to have a four walled Sukkah[4] [that does not contain any opening other than the door[5]] and so is the custom.[6] At the very least, one should try to have three complete walls.[7]
Complete walls versus walls with breaches: It is customary to make complete walls rather than walls that contain breaches.[8] If one is unable to make four complete walls then it is better to make three complete walls and have one side be open without a wall than to make four walls with breaches.[9] Nevertheless, in such a case, it is customary to make a Tzuras Pesach by the fourth wall, as explained next.
Making Tzuras Pesach by fourth wall:[10] By a three walled Sukkah, it is customary to make a Tzuras Pesach by the fourth wall for beauty purposes.
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According to the custom of building four walls, can one use the rule of Lavud for these walls?[11] According to the custom, one is to make four complete walls without resorting to the rule of Lavud. However, from the letter of the law, it suffices even if all four walls are Lavud, as will be explained in Halacha E.
If on Shabbos or Yom Tov the walls blew off due to wind and invalidated the Sukkah, may it be replaced? No. See Halacha 2B in Q&A!
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[1] Michaber 630:2; Mishneh Sukkah 2a; Tana Kama in Braisa Sukkah 6b
Other Talmudic opinions: Rebbe Shimon is of the opinion that from the letter of the law one must have three walls, and a fourth wall of a Tefach. [Braisa Sukkah 6b]
A Sukkah made with two walls pointing diagonally [like this <]: Some say that it should be viewed as three walls, however the space in the corner which does not contain 7Ă—7 Tefachim is invalid to sit in. [See Chazon Ish Eiruvin 72:5; Piskeiy Teshuvos 634:2]
[2] See Halacha C that in truth, through the rule of Lavud, it is possible to make a Sukkah with even only one complete wall.
[3] Concept of lavud with three strings within three tefach of each other. Opinion of M”A that argues no lavud unless three walls. Opinion in Shua not to make plastic sheet sukkahs.
[4] Admur 638:2 “If he made four complete walls…without mentioning which one was made for the Mitzvah Min Hamuvchar”; Shelah Miseches Sukkah; Beis Hashoeiva; P”M 643 M”Z 4; Chayeh Adam 146:3; Alef Hamagen 626:1; Nitei Gavriel 11:1
Other Opinions: Some Poskim rule that it is a Mitzvah Min Hamuvchar to have three complete walls. [M”B 630:28] Thus according to them even initially there is no need to have four walls. Other Poskim suggest that according to Kabbalah, one only have two walls and a Tefach. [Mishnas Yaakov 630 in name of Maharshak]
[5] See next regarding complete walls versus breached walls, and M”B 630:28 in name of Maharitz Geios
[6] Admur 639:10 “Today the custom is to make four walls for the Sukkah”; Sefer Haminhagim p. 65
[7] M”B 630:28 in name of Maharitz Geios; See Rama 630:4 “Better to make three complete walls than four with breaches”
[8] Rama 630:5
[9] Rama 630:5
[10] Rama 630:3; Taz 630:4; M”B 630:19
[11] Rama ibid and M”B 630:28 that three of the walls are to be made complete without resorting to Lavud and Tzuras Pesach, and M”B ibid in name of Maharitz Geios that aside for the door, it is a Mitzvah Min Hamuvchar for the rest of the Sukkah to be completely closed up from all its directions.