1. The Prohibition of dyeing clothing and other objects:[1]

A. The dye is lasting:

Biblically: There is only a Biblical prohibition [involved in dyeing] when dyeing with a permanent dye, however a dye which will not last at all[2], such as one who placed vermillion [a bright red pigment], or rouge[3] on metal and copper and [thus] dyed it, is not liable because one is only coloring it temporarily and is thus not dyeing anything.

Rabbinically: Nevertheless, doing so is Rabbinically forbidden.

B. Hastening the dyeing of a product and adding dye:

Mixing a pot that contains wool and dye:[5] It is Biblically forbidden to mix a pot of wool with dye, even if the dye has been fully cooked before Shabbos[6], and the wool has received the dye[7], due to the dyeing prohibition.[8] [From here we can learn that it is forbidden to a) Hasten the dyeing of a product, and b) Thicken the dye of a product.]

C. Making dye on Shabbos:[9]

It is forbidden to make dye on Shabbos, such as by soaking pigment in water, [due to the dyeing prohibition[10], or alternatively due to the kneading prohibition[11].]

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[1] Admur 320:28; M”A 320:25; Rambam 9:13; Machatzis Hashekel 320:24; M”B 320:59

Av Melacha: The Av Melacha of dyeing in the Mishkan was with the dyeing of the tapestries and curtains used for the Mishkan’s walls and tent.

[2] This implies that if the dye will last some time, or some of the ink will penetrate and remain, then it is Biblically forbidden even though it will not last forever, and so is implied from the fact the Poskim rule that dyeing the human body is Rabbinical only because it is skin and not because it will not last forever.  

^[3] Reddish makeup for cheeks

[4] As is understood from Halacha 3 below.

[5] Admur 252:2 and 318:30 in parentheses; Michaber 318:18; M”A 318:43; Taz 318:22; M”B 252:5 and 318:116; Regarding why in Admur 318:30 he writes the “dyeing prohibition” in parentheses-see “The reason”

[6] Admur 252:2

[7] Admur 318:30; Michaber ibid

[8] The reason: As the mixing causes the dye to become more absorbed into the wool. [Admur 252:2; 2^nd answer in Rosh; M”B 318:116] Alternatively, the reason is because constant mixing is part of the dyeing process, in order to prevent the wool from burning. [Admur 318:30; Ran, brought in M”B 318:116] Alternatively, mixing a hot pot of dye is forbidden due to the cooking prohibition, as dye is never fully cooked. [Rosh in 1^st answer, brought in Taz ibid; Shaar Hatziyon 318:138] The practical ramification is regarding whether one may mix a pot of dye that is fully cooked, even if there is no wool inside. [Shaar Hatziyon ibid] Based on all this it is understood why Admur placed his ruling in 318:30 in parentheses, as there are opinions that say the prohibition is due to cooking. As for why Admur mentions two different reasons in 252:2 and 318:30, as well as only in 318:30 he places the ruling in parentheses, seemingly the explanation is as follows: In 352:2 the case is discussing that the wool has not yet fully absorbed the dye, and hence according to all there is a dyeing prohibition involved. However, in 318:30 in which the wool has fully absorbed the dye, Admur states the reason is because it is “the way of the dyers to prevent the item from burning”, however in this matter he was in question and hence placed the ruling of “due to the dyeing prohibition” in parentheses.

[9] Magen Avraham 320:25 brought in Mishneh Berurah 320:59; 252:1; Michaber and Admur 252:1 that doing so is only permitted from before Shabbos.

[10] As rules Rambam 9; Opinion of Rebbe Yossi Bar Rebbe Yehudah in Shabbos 18a, and so rules Michaber in Shulchan Aruch [321:14] that there is no kneading prohibition involved in simply adding water to kneading material.

[11] As rules Raavad based on Rebbe Yehudah Hanassi Shabbos ibid that there is a kneading prohibition involved even in simply adding water to kneading material; brought in M”A ibid and M”B ibid