Maybe I should welcome myself back. I haven't posted in awhile mainly due to a combination of summer, work and laziness. (I won't say what was the ikkar and what was the tafeil). I will bli neder try and post more consistently this year but as always I make no promises.
The members of my chaburah asked me to give a shiur during the Yom Kippur break. I spoke about the mitzvah of building a sukkah. Just as a side note, I found that giving the shiur invigorated and energized me for the rest of the day.
There are a number of mekoros which seem to indicate that there is a mitzvah to build a sukkah.
1) Rashi Makkos 8a. Both the Avnei Nezer (459) and Netziv in Ha'Emek Sheilah Parshas Zos Haberacha point out that Rashi seems to hold there is a mitzvah to build a sukkah. The gemara says that if you chop wood and kill someone you are chayav golus even if you are chopping wood to build a sukkah. Rashi writes that chopping the wood is not a mitzvah but building a sukkah is.
2) The Shi'iltos (V'Zos HaBeracha) writes it is a mitzvah to make and sit in the sukkah. The Netziv is medayeik that making a sukkah is also a mitzvah. The m'kor is from the possuk "
3) The Yerushalmi (quoted by Tosafos Sukkah46a) says one makes a beracha on making the sukkah. It would seem from here that it is a mitzvah to build a sukkah. The Minchas Elazer points out that the Bavli in Menachos 42a disagrees and holds there is no beracha on making a sukkah and therefore the Bavli will tell you there is no mitzvah to make a sukkah. However, one could argue that the machlokes Bavli and Yerushalmi is whether one makes a beracha on a mitzvah that is not finished. Since the complete mitzvah is sitting in the sukkah the Bavli will hold you don't make a beracha.
4) The gemara says one makes a She'hechiyanu on building a sukkah. The Aruch LaNer says that this only makes sense if you hold building a sukkah is a mitzvah. However, one could argue that the SHehechiyanu really goes on the sitting in the sukkah but we make it by the asiyas sukkah since you need toi build a sukka to be able to sit in it.
5) The Chasam Sofer (Yora Deia 471) and Minchas Elazar hold there is no mitzvah to build a sukkah
1) The Netziv says the klal of Mitzvah Bo Yoseur M'Bishlucho applies to building a sukkah. Furthermore, if one plans on using his friends sukkah there would still be a kiyum mitzvah to build your own.
2) The Rema based on the Maharil paskens (Hil Sukkah 655) that one should build a sukkah right after Yom Kippur because Mitzvah HaBa'ah L'Yodcha AL Tachmitzena.
3) The halacha is that a sukkah built by a non Jew is kosher but the poskim write that one should try and add on to it. The Moadim U'Zmanim says the reason for this is because it is a mitzvah to build a sukkah.
4) Genrally speaking, the Shehechiyanu we recite on the first night goes on the Zman and on building/sitting in the sukkah. If one sat in a neighbors sukkah the first days and then built his own sukkah on Chol HaMoed does one make Shehechiyanu. The Mikroei Kodesh says that if you hold there is no mitzvah to build a sukkah then there is no question-of course there is no Shehechiyanu. The Shehechiyanu is only going on the yeshivas sukkah and the zman of sukkos both which were covered on the first night. If you hold there is a mitzvah to build a sukkah then you can start to ask.