It is Biblically forbidden to make a Tattoo on one’s skin.
Definition-How its done: The tattoo [that is forbidden by the Torah] is made by making a cut in one’s skin and then filled it with sand or ink or other pigments that leave a mark. Alternatively, one first marks an image on the skin using a pigment and then cuts open the skin for the ink to enter into its pours. [Today tattoos are made through first sketching an image onto the skin and then using a fine needle that is filled with ink to puncture the skin and enter the ink. Thus the cutting and filling is done simultaneously.]
Where on the skin? The Biblical prohibition against making a tattoo applies to anywhere on the skin.
What writing is forbidden? The Biblical prohibition against making a tattoo applies to any type of writing. [It however only applies to letters of a language and does not apply to making a mere mark or line and the like, although doing so is Rabbinically forbidden.]
Having someone else do it: If someone else makes a tattoo on one’s skin then if he assisted him in the tattooing he is liable. If he did not assist him in making the tattooing then he is exempt from Biblical liability. Nevertheless, it remains Rabbinically forbidden.
Why did the Torah prohibit tattoos?
May one write a tattoo onto the skin of a gentile?
May one write on one’s skin?
May one with a tattoo be buried in a Jewish cemetery?
 Shulchan Aruch 180; Mishneh Makos 21a
 Chinuch Mitzvah 253
 Michaber 180/1; Mishneh Makos 21a that one must both cut and fill it with ink
 Shach 180/1; Bach
 Shach 180/2
 Shach 180/2
 Meil Tzedaka 31, brought in Pischeiy Teshuvah 180/1
 Michaber 180/2 and 11
 Shach 180/4
 Michaber 180/3
 Taz 180/1; Shach 180/5
 The reason: As the wound shows that it was not done for the sake of tattooing as do the idol worshipers, but rather for healing purposes. [Shach 180/6; Taz 180/1] Even after the wound heals there is still some mark left of the wound which shows the intent of the remaining ink mark. [Taz ibid]
 Shach 180/6; Chinuch Mitzvah 253
 Noda Beyehuda Tinyana, brought in Pischeiy Teshuvah 180/2
 See Minchas Chinuch Mitzvah 253/1; Nishmas Avraham Y.D. 180
 Michaber 180/1; Mishneh Makos 21a
 Minchas Chinuch ibid based on Beis Shmuel E.H. 124/16 “Even if the witnesses just wrote their signatures and did not fill it with ink, nevertheless they become Rabbinical Reshaim” [However see next footnote for alternative explanation of Beis Shmuel]; Implication of Rambam in Avodas Kochavim 7 who writes exempt; Implication of Tosafus Gittin 20b
 The law if the ink is erasable with time: The Minchas Chinuch ibid writes that even according to the stringent opinion, the Rabbinical prohibition is only regarding ink that is not erasable, however if the ink is erasable then the prohibition does not apply. So records also Shevet Halevi 3/111-1 in name of Minchas Chinuch. See however Pashegen Hakesav of Rav Chaim Kanievski p. 74-75 that such ink does not exist, as all writing on skin is erasable and hence one must conclude that according to the stringent opinion, any writing on the skin is Rabbinically forbidden. So is also implied from the Mishnas Chachamim brought in next footnote that accoridngt o the stringent opinion any writing is forbidden Rabbinically.
 Mishnas Chachamim 57; Kesef Mishneh on Rambam ibid; Shevet Halevi 3/111-1 that all the above Poskim in previous footnote, recorded by the Minchas Chinuch ibid only referred to one who made a cut into the skin and did not fill it with ink, in which case it is Rabbinically forbidden, however to simply write on the skin without making any cut was never discussed by them and there is thus no such source to Rabbinically prohibit it [Rav Chaim Kanievsky, brought in Nishmas Avraham ibid makes the same claim]; Implication of the Poskim who all omit the above Rabbinical prohibition against writing on the skin even without cutting it, including the Michaber 180, Chochmas Adam 89/11; Kitzur SHU”A 169/1; Ben Ish Chaiy Maaseiy 2/15
 Rav SZ”A, brought in Nishmas Avraham ibid, rules one may be lenient even initially; Rav Chaim Kanievsky, brought in Nishmas Avraham ibid that the Achronim write the custom is to be lenient; See Minchas Chinuch ibid that even according to the stringent opinion, if the ink is erasable it is permitted. [see previous footnotes]
 As rules the Minchas Chinuch ibid; To note however that to date there does not exist any ink that permanently remains on the skin with simply writing on it, without cutting into the skin with a needle and the like. If such a thing existed the entire tattoo industry would change to this method which is painless and woundless.
 See Yoreh Deah 362/5; Sanhedrin 47a that one is not to bury a Rasha next to a Tzaddik, which is the source we find for the custom of having a Jewish cemetery that is free of gentiles. It would likewise based on this be prohibited to bury a Rasha who is a Jew near a gentile, and hence one with a Tattoo may not be buried with gentiles even though he has committed a sin. See Igros Moshe 147 that even a Jew who is married to a gentile must be buried in a Jewish cemetery.