Women wearing socks:
It is forbidden for men to learn Torah or Daven opposite a woman’s legs [literally, Shoka] as the legs are considered an area of privacy by a woman, and is therefore an Erva to be revealed. [It is therefore necessary for women and girls to cover their legs when they are in view of other men.]
Definition of Shoka/legs and what area of the legs must be covered: The term Shoka in modern Hebrew is translated today as the leg, or shinbone, and reaches up until the ankle. However, the Halachic definition of this term is obscure and hence disputed amongst Poskim. Some Poskim learn that the Shoka includes the entire leg, from her thighs all the way down to the toes on her feet, and thus it is forbidden for men to learn and pray in sight of these revealed areas, and consequently women must be modest to cover these areas as well. Other Poskim however learn that the Shoka only includes the legs up until the ankle, while the actual feet are not included, and do not have to be covered. Other Poskim rule that the Shoka only includes the thighs, until the knees, while from the knees and down is not included, and does not need to be covered in areas that are not accustomed to do so. Practically, majority of Poskim negate the latter opinion, and rule that even the feet must be covered in all areas, and so is the implied opinion of Admur, and so is the custom amongst all Chareidi Jewry and one may not be lenient in this matter. Furthermore, even according to the lenient opinions, in an area that the custom is to be stringent, they too agree that one must be stringent and abide by these forms of modesty.]
See through socks/stockings: If a woman is wearing sheer clothing [i.e. see-through] and her flesh is visible through it, it is forbidden to learn and Daven in her presence, just like is the law if she was not covering it at all. [See Q&A for how many denier is defined as valid and not see through]
According to majority of Poskim, and the ruling of Admur, women and girls are required to cover their legs and feet with socks/stockings when out in public or in the presence of other men. Even those who are lenient to not cover the feet and/or legs, must cover it when in a community that is stringent. It is forbidden for a man to learn Torah or Daven in the presence of woman whose legs are uncovered.
How are the legs to be covered?
The area of the legs that are below the knees may be covered with stockings and are not required to be covered with a skirt. However from the knees and above must be covered with a skirt, even if one is wearing stockings that cover this area. The knees must remain covered even when sitting.
How many deniers should the stockings be?
It is forbidden to wear transparent stockings that allow the skin to be seen. Therefore, according to the stringent opinion above and the ruling of Admur that the legs must be covered, the stockings must be dense enough cover all the skin and opaque enough to block sight of the legs. In terms of deniers this would match a very high number, such as 70/80, and would not allow skin color stockings. Practically, while some Chassidic communities follow this ruling, the majority of Jewry is accustomed to allow the wearing of even lesser dense stockings that are skin color. The reason for this is because even skin color stockings blur the sight of the actual skin, and this suffices in this regard. The accustomed Rabbinical directive is to wear no less than 40+ deniers. However, some are lenient to wear even up until 20 denier. Seemingly however, this is invalid according to the astringent opinion, and ruling of Admur.
From what age are girls to begin being careful to wear socks?
Girls must begin to be careful to cover their legs starting from three years of age. One should not be oppressive about this and should speak in a pleasant way.
May one walk around without socks in the summer?
There is no leniency given in this regard in the summer versus the winter. Nevertheless, in the privacy of one’s home, when men are not present, it is permitted to walk without socks.
May one be lenient to walk around at home without socks?
If there are men in the area, including a father or brother, then one is not to do so. If however there are no men at home, then one may be lenient. A wife may be lenient in front of her husband at times that she is not a Nida.
If one is wearing a long skirt that reaches her ankles, must she still wear stockings?
No. If however the skirt lifts up when she sits or bends and her skin can be seen then knee high stockings are to be worn.
 Admur 75/1; Rav Chisda in Brachos 24a
 This is necessary in order to not cause men to stumble in forbidden thoughts, as well as so they not transgress learning or Davening before an Erva.
 See Mishneh Ohalos 1/8 and Mefarshim there; Rashbam Baba Basra 57; Mishneh Keilim 14/8 and Mefarshim there; Piskeiy Teshuvos 75/4; Halichos Bas Yisrael 4/4 footnote 12
 Simple implication of Admur ibid “Although the Shoka is not a private area by a man as it is customary for it to be revealed in areas they walk without Anpalaot/socks”; Implication of Mishneh Ohalos ibid according to many Mefarshim; Implication of Michaber Y.D. 194/10; Makor Chaim 75/1; Shut Rav Akiva Eiger Tinyana 28 based on Tosafos Menachos 37a; Tzur Yaakov 2/1; Chasam Sofer E.H. 69; Shulchan Hatahor 75/1 based on Zohar Naso 142 that “a Shoka of a woman is an Erva and the leg of a woman is an Erva”; Mahariy Shteif 43
 Simple implication of Chayeh Adam 4/2 “The bottom of her feet [Parsos Ragleha] in areas that women walk barefoot may be revealed.” [So understands Shevet Halevi 1/1 and Beis Baruch on Chayeh Adam and Piskeiy Teshuvos 75/4. However, see Shaar Hatziyon 75/4 who seemingly learns the Chayeh Adam permits until the knee, Vetzaruch Iyun]
 P”M 75 M”Z 1 “It is known that the Shoka is from the knee and up [thigh] and thus it is possible that from the knee and down in areas that women walk with this area revealed, it is permitted.” [See however Shut Magidos 24]; M”B 75/2 and Shaar Hatziyon 75/4; [Rules based on P”M ibid that it is permitted, even though the P”M only suggested this matter.]; Igros Moshe E.H. 4/100; Kovetz Tehsuvos of Rav Elyashiv1/13
 Salmas Chaim 88; Minchas Yitzchak 6/10; Divrei Yatziv 37; Beir Moshe 8/1; Shevet Halevi 1/1; 3/91; Chazon Ish 16/8 [however he later states that it is difficult to rule on this matter]; Az Nidbaru 7/3; Piskeiy Teshuvos 75 footnote 26
 As is evident from the continuation of Admur ibid that although men are accustomed to walk around barefoot, in those areas that they walk without socks, nevertheless by a woman it is considered a modest area. Thus, we see that it includes also the feet.
 Piskeiy Teshuvos 75/4
 M”B 75/2
 Admur 75/3; M”A 75/1; Bahag Brachos 3
 See Halichos Bas Yisrael 4 footnote 12 who learns that according to the Poskim who rule the legs are part of the Shok, then the legs must be entirely covered by a skirt and those lenient to wear stockings are following the opinions who rule the Shok is not the legs. However in truth, nowhere does it say that the legs or skin must be covered by a specific form of dress, and this matter is seemingly relevant to Das Yehudis, in accordance to community custom, as well as provocative areas. Thus, since from the knees and above is a provocative area for a man even when covered, therefore it must be covered in a way that its shape is not seen. However the area of the legs which are below the knees, and don’t cause as much provocation to men, may be covered in a way that shapes the legs. [See Igros Moshe ibid; Rav Zilber in Malbushei Nashim p. 11, brought in Halichos Bas Yisrael ibid footnote 11]
 Halichos Bas Yisrael ibid in name of Poskim; See Igros Moshe ibid
 Halichos Shlomo ibid; Halichos Bas Yisrael ibid in name of Poskim
 See Piskeiy Teshuvos 75 footnote 27
 Based on Admur ibid; Mishneh Halachos 12/5; Az Nidbaru 10/34; Poskim in Piskeiy Teshuvos ibid;
 Piskeiy Teshuvos ibid
 Satmar and other Hungarian Chassidic communities
 See Igros Moshe E.H. 4/100; Halichos Shlomo 2/12 in name of Rav SZ”A
 Igros Moshe ibid “In truth the skin is not really viewable through the stockings and it only seems so due to the camouflage color. The proof is that if the stockings were to be black then in truth it would not even appear to others that they are seeing the skin”; Halichos Shlomo ibid
 Piskeiy Teshuvos ibid
 Chayeh Adam; Biur Halacha 75/1 “Tefach Megula” in name of Shulchan Shlomo; Ketzos Hashulchan Vol 1, Haaros Page 90; Shut Daas Sofer; Likutei Sichos [18 p 448] and other prominent Rabbis of this generation; See letter of Rav Farkash in “The Jewel of our Crown” page 79
Other opinions: However, the Chazon Ish rules that the laws of modesty only begin at a later age [6/7].
 Halichos Shlomo 2/12 in name of Rav SZ”A
 See Halichos Shlomo 2/12 in name of Rav SZ”A; Minchas Yitzchak 6/10;
 See Shevet halevi 5/77