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The reason and meaning behind wearing a Yarmulke:
There are numerous reasons brought in Admur behind wearing a skullcap. These include:
- Fear of heaven
- Not to follow the statutes of the Gentiles
- To openly appear like a Jew.
Modesty:  Wearing a covering on one’s head is an attribute of modesty and holiness. For this reason by the morning blessing said regarding wearing a hat, the term used is “Oter Yisrael Bisifara”, as by Jews the hat is not worn for physical enjoyment, as is by gentiles, but for a spiritual purpose.
To cover the normally covered parts: Today, in our times, since it is common for everyone to always cover their heads it is always forbidden to walk, or even sit,with one’s head uncovered, as by doing so one reveals an area of the body which is commonly covered, and it is thus immodest.
Drawing down fear of heaven: Wearing a Yarmulke represents fear of heaven and by wearing it one draws upon oneself heavenly awe. [Alternatively it is done out of respect for the Shechina which resides over one’s head.]
Not to follow the gentiles: In today’s times that the gentiles walk bareheaded while the Jews which are holy cover their head due to modesty, certainly it is an obligation for one to cover his head, and one who walks or even sits without a head covering, like a gentile, transgresses the command of “In their statutes do not follow”. [As well in today’s times wearing a skullcap has additional meaning, being that it represents to others that one is Jewish and holds on to the Jewish faith. Thus this mitzvah is unique being that it is connected to the identification of us being the chosen people.]
 Basra ibid
 Kama ibid
 Lit “al rosho”
 Moreh Nevuchim 53 brought in Taz 8/3; Machatzis Hashekel 2/6; See Likkutei Dibburim Likut 32
 Basra ibid based on Taz 8/3
 This latter statement is missing in many versions of the Shulchan Aruch due to censorship. It does however appear in the original publishing of the Shulchan Aruch and has been reinserted in the new publishing of Kehos.
 Rebbe in Shaareiy Halacha Uminhag vol. 5 page 26