Shulchan Aruch Chapter 9: What Garments Require Tzitzit and Which Are Exempt From Tzitzit (6 Paragraphs)
1. Biblically, the only garments that require tzitzit are clothes made out of linen or wool from a sheep. But garments of other materials only Rabbinically require tzitzit. [There are those who claim that all garments Biblically require tzitzit and so is the Halacha.]
2. Fringes made from linen or lambs wool can be used on garments of any material with the following exception: fringes of linen for a garment of wool, or fringes of wool for a garment of linen. This is due to the fact that today, we don’t have תכלת so it is then considered כלים. [Some say that one should never use tzitzit made from linen even with other garments (not wool) and such is our custom.]
3. Fringes made from other materials can only cover (garments made from) the same material. For example, (fringes of) silk are used for a garment of silk and (fringes made with) wool from a grape vine can only be used for the same material garment. However, if these are put different material garments, they are not מפטר (it is invalid).
4. If one was wearing a טלית made from other materials, then added some fringes made from the same material of the garment and other fringes made from lambs wool or linen, this is questionable.
5. There are authorities who maintain that one needs to make tzitzit colorful with the same coloring of the טלית and the very careful people have this custom. [The Ashkenazim do not have the custom to do this for tzitzit except for children. We don’t even do this with colored garments and one need not change.]
6. There are those who claim that one shouldn’t make a טלית out of linen even thought the Halacha is not like this. One fearful of heaven would satisfy everyone and make a טלית out of sheep’s wool that Biblically requires tzitzit without doubt. [However, if one only has a טלית of linen, it is better to use this garment and (even) tzitzit made from linen then to be מבטל the mitzvah of tzitzit.]
Translated by Jay Dinovitser
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 M.B. says wool from a ram is also included.
 Lit. “make פטור all types of garments”
 Wool dyed with a special blue dye made with the blood of some secret animal. This species was forgotten in exile. It says in the Torah, that the tzitzit should contain some of this blue wool. However, there are those who claim to have proof that it is a certain snail with blue blood (since archaeologists uncovered piles of this snail in a town mentioned in the Talmud famous for making blue wool) and sell this blue wool. All authorities agree the lack of blue wool does not make the tzitzit invalid.
 Mixing of wool and linen in a single garment is Biblically forbidden and is called כלים.
The following is a logical explanation for this concept: The Torah says that any garment requiring tzitzit should have blue wool, so if one adds this to a linen garment, it is not considered a forbidden mixture. Once blue wool is added to linen, one can add additional strands of regular wool (fringes). However, today where we don’t have the blue wool, this does not apply.
 M.B. says that the use of colored tzitzit are due to “this is my G-d and I will glorify him”. Some authorities claim that the Tzitzit must be similar to the corners of the garment. Therefore, the corners of the garment should be white if one is using white tzitzit in order to satisfy all authorities.
I personally have seen someone wearing a multi colored Talit with orange, pink and other bright colors. Nowadays, most טליתים have blue or black stripes (with gold and silver) and many have silver crowns or decorations due to the concept of glorifying the mitzvah. However, I have yet to see colored fringes. On all טליתים, there are white squares sown on all of the corners as the Mishna Brura advises.
 M.B. says the reason for this opinion is to not accustom the masses to use linen fringes. For if they were to use it, they would unknowingly place it on a wool garment and have a forbidden mixture of wool and linen.
An obvious question is, why are we worried about people putting linen fringes on wool garments and not worried about placing wool fringes on linen garments? The answer is that linen garments are very expensive and are rarely used for a טלית while wool garments are common since wool is cheap. Therefore, there is a greater concern of mistakenly putting linen fringes on wool garments.