Gemara

Hairs grow from the roots.

Support: There are old people who dye their beards (black). The part of the hair near the roots is white!

59a (Beraisa) Suggestion: Perhaps "Lo Yihyeh Kli Gever Al Ishah (v'Lo Yilbash Gever Simlas Ishah)" forbids a woman to wear a man's garment, and vice-versa!

Rejection: The Torah calls this "To'evah" (but this is not an abomination).

Answer #1: A man may not wear a woman's garment and sit among women, or vice-versa.

Answer #2 (R. Eliezer ben Yakov): A woman may not bear weapons in war, and a man may not adorn himself like women do.

Shabbos 94b (Beraisa): All agree that one is liable on Shabbos for removing one white hair among black hairs (for he is insistent to remove it). A man may not do so even during the week because it says "v'Lo Yilbash Gever..."

129a (Beraisa): One may not look in a mirror on Shabbos (lest he cut uneven hairs);

R. Meir permits to look in a mirror fixed on the wall.

Question: Surely, R. Meir permits a fixed mirror because (by the time he gets a scissors) he will remember that it is Shabbos. The same applies if it is not fixed!

Answer: They argue about a metal mirror:

(Rav Nachman): One may not look in a metal mirror lest one (use its edge to) cut dangling hairs (he need not delay to get a scissors).

Rishonim

The Rif and Rosh (Shabbos 36a and 10:3) bring the Gemara in Shabbos.

Ran (Avodah Zarah 9b DH Ro'eh): Where men look in mirrors, it is permitted. Only Chaverim refrain. A Tosefta teaches that R. Gamliel's house was permitted to look in mirrors. This is because they were Chaverim, and normally they would refrain.

Question (Gra YD 156:7): Perhaps in that place, only women used mirrors!

Keneses ha'Gedolah (YD 182:6): The Gemara permitted one being shaved by a Nochri to look in a mirror. What forced the Ran to permit everyone (where men do so)? He holds that if it were forbidden, we would not permit it in order to enable being shaved by a Nochri! Other Poskim disagree. They hold that the Isur is mid'Rabanan. Chachamim limited their decree as they saw fit. The Ran cannot say so, for he forbids mid'Oraisa.

Rambam (Hilchos Avodah Zarah 12:9): Removing hair from other parts of the body, e.g. the underarms and genital area, is forbidden mid'Rabanan. One is lashed for it. This is in a place where only women remove it, for it is Tikunei Ishah (adorning like a woman). In a place where men remove it, he is not lashed.

Rambam (10): A man may not wear women's clothing, e.g. colored clothing or gold necklaces, in a place where only women wear them. We follow the local custom. If he wore women's clothing, he is lashed. One who removes one white hair out of black hairs in his head or beard is lashed for Bigdei Ishah.

Rebuttal (Ra'avad): The Gemara forbids removing one hair, but surely he is not lashed. This is not Tikunei Ishah. It is not Nikar (noticeable) at all!

Beis Yosef (YD 182 DH v'Im): The Rambam rules like R. Eliezer ben Yakov, who says that "v'Lo Yilbash Gever" forbids Tikunei Ishah. The Gemara did not discuss lashes, but surely R. Eliezer obligates lashes. If the Ra'avad holds that removing one hair is not Tikunei Ishah and is not Nikar at all, why is it forbidden? I say that it is Nikar if only one hair on the head is white! The Rambam obligates even when there are many white hairs, since it is Tikunei Ishah when it is Nikar.

Gra (YD 182:13): The Gemara says that (all) removal of hair is only mid'Rabanan. This is why the Ra'avad exempts from lashes.

Rambam (ibid.): The same applies if he dyed his hair black. He is lashed even for one hair.

Tosfos (Avodah Zarah 29a DH ha'Mistaper): Shabbos 129a forbids looking in a mirror on Shabbos. This implies that during the week it is permitted. This refers to women. Men may never look in a mirror, due to "Lo Yilbash Gever." The Targum of this verse is 'a man may not adorn himself like a woman.'

Ritva (Makos 20b DH v'Davar): '...Because it says "v'Lo Yilbash Gever"' connotes that the Isur is only mid'Rabanan. This is like Chachamim, who forbid mid'Oraisa only women's garments. Alternatively, it is mid'Oraisa. The Tana was not precise.

Poskim

Shulchan Aruch (YD 156:2): A man may not look in a mirror due to Lo Yilbash Gever. It is permitted only for medical reasons, e.g. his eyes hurt, or if he cuts his own hair, or a Nochri cuts his hair in private, and he looks in it to appear distinguished.

Bedek ha'Bayis (DH v'Chen): Tashbatz Katan (546) permits when cutting one's hair, lest he cut himself. When Rabbeinu Meir's eyes hurt, he would cover the rest of his face and look in a mirror.

Rema: Some say that it is forbidden only where only women look in mirrors, due to Lo Yilbash Gever. Where also men do, it is permitted. Even where it is forbidden, it is permitted for healing one's eyes, removing stains from his face or feathers from his head. This is the custom.

Source (R. Zalkil, cited in Darchei Moshe 1): One may look in a mirror to, remove stains from his face or feathers from his head, for he intends to avoid disgrace, not to beautify himself.

Shulchan Aruch (YD 182:6): A man may not remove even one white hair amidst black ones, due to "Lo Yilbash Gever." Similarly, a man may not dye even one (white) hair black.

Beis Yosef (DH v'Chen): The Tur says that the Rambam obligates one who dyes black hair white. Indeed, this beautifies a man, but it is not the way of women to make themselves look older, rather, younger! The Rambam obligates only one who dyes white hairs black.

Taz (7): This is a scribal mistake in the text of the Tur.

Note: The Chazon Ish did not consent to a Bochur whose hair turned white to dye it black to avoid shame (Ma'ase Ish p.167). Igros Moshe (YD 2:61 DH uv'Im) permits in order to get a job, if he can work as well as a young man.

Shulchan Aruch (ibid.): Similarly, a man may not look in a mirror.

Ginas Veradim (60:12, cited in R. Akiva Eiger): Where also men look in mirrors, it is permitted. Very pious people refrain everywhere.

Igros Moshe (ibid., DH Hinei): Merely looking in a mirror does not fix one's appearance, but it shows excessive concern for beauty. Looking itself gives importance. This is why it was permitted to one who is shaved by a Nochri!