The Hebrew term kareth ("cutting off") is derived from the Hebrew verb karat ("to cut off"). The noun form does not occur in the Hebrew Bible. The plural, Kerithoth ("Excisions"), is the seventh tractate of the fifth order Kodashim of the Mishnah. In the Talmud kareth means not necessarily physical "cutting off" of life but extinction of the soul and denial of a share in the world to come.
Hebrew Bible 
Rabbinical literature 
It is the punishment for serious crimes, some of which are also punishable by death by a human court. Kareth can mean dying young (before the age of 60), dying without children, or the soul being spiritually "cut off" from your people after death. According to Nachmanides both definitions are accurate, and are applicable according to the nature of the person that committed the offense. If he was generally a good person, meaning that the good in him outweighed the evil, he is punished with dying before his time, unless he had other virtues that are cause for him to merit living out his full life, but retains his portion in the world to come. However if the evil in him outweighed the good, he is then granted a good and lengthy life to reward him for the good that he did in his life, but upon death he will have no portion in the world to come. The medieval scholar Rabbi Yonah Gerondi in his famous ethical work The Gates of Repentance says that the Torah itself makes a distinction as to which form of kareth is to be applied for a particular offense. In most cases the Torah uses the term such as that in Leviticus 18:29; the persons who commit them shall be cut off from among their people, which he says is a reference to a punishment in this world. However when the Torah uses a term such as that in Numbers 15:31; that person will be cut off completely, his offense will remain with him, that penalty refers to being spiritually cut off after death.
There are two opinions as to what the nature of being spiritually cut off means in reference to the soul after death. Maimonides is of the opinion that this means that upon his death the "soul that left his body is completely destroyed and he dies the death of animal". Nachmanides maintains that the soul is not destroyed, but that the soul being cut off after death is a reference to the spiritual world where after death the soul exists in an exalted spiritual state, and that the penalty of Kareth is that he is not eligible to enter into that world. However the soul lives on and is eligible for the Resurrection of the dead.
Kareth is applicable only when the transgression was done on purpose, and without later proper repentance, and is applicable only to Jews. When done unintentionally, such a transgression generally requires that a sin-offering be brought.
Offenses punishable by kareth 
According to the Mishnah in Kerithoth (1:1) there are a total of 36 offenses punishable by kareth. These are the 36 offenses as enumerated in that Mishanh. Where the offense is sexual intercourse kareth applies to both parties:
- Sexual intercourse with one's mother
- Sexual intercourse with one's father's wife
- Sexual intercourse with one's son's wife
- A male having sexual intercourse with another male
- A male having sexual intercourse with an animal
- A female having sexual intercourse with an animal
- Having sexual intercourse with both a mother and her daughter within the span of his lifetime
- Sexual intercourse with a married woman
- Sexual intercourse with one's sister
- Sexual intercourse with one's father's sister
- Sexual intercourse with one's mother's sister
- Sexual intercourse with the sister of one's wife
- Sexual intercourse with one's brother's wife
- Sexual intercourse with the wife of one's father's brother
- Sexual intercourse with a menstruating woman, known as a nida(נדה)
- Cursing God using the appropriate holy name, known as megadef (מגדף)
- Worshiping a deity other than God, known as Avodah Zarah (עבודה זרה)
- Sacrificing one's child to Moloch (מלך)
- Consulting with a spirit through a process known as ohv (אוב)
- Violating the Shabbat (שבת) by doing one of the 39 categories of activities prohibited on Shabbat
- Eating of an offering while in a state of ritual impurity, known as tumah (טומאה)
- Entering the temple or Tabernacle while in a state of ritual impurity, known as tumah (טומאה)
- Eating of a form of animal fat known as chelev (חלב)
- Eating or drinking blood
- Eating of an offering after the allowable time for the eating of that offering has expired. An offering in this state is known as notar (נותר)
- Eating of an offering that was offered with the intention of eating of it after the allowable time for the eating of that offering has expired. Such an offering is known as pigul (פיגול)
- Slaughtering an offering outside the boundaries of the temple or Tabernacle
- Offering up an offering upon an alter outside the boundaries of the temple or Tabernacle
- Eating chametz on Passover
- Eating or drinking on Yom Kippur
- Violating Yom Kippur by doing one of the 39 categories of activities that are prohibited on Shabbat
- Creating a replication of the holy anointing oil (שמן המשחה) that was used for the anointment of high priests and kings of the house of David that was made by Moses, using the same ingredients and precise measurements, and creating it in the same volume as created by Moses 
- Creating a replication of the incense offering, known as the Ketoret (קטרת), using the same ingredients and precise measurements of the Ketoret
- Anointing oneself with the holy anointing oil that was created by Moses
- Failure to bring the Passover offering
- Failure to circumcise oneself
- The Talmud with English translation and commentary: Volume 1 A. Zvi Ehrman 1965 "Kareth means not necessarily physical dissolution but extinction of the soul and its denial of a share in the world to come. This exposition, stemming from Rav's saying on our page, is usually deemed the accepted Jewish view on the ..."
- Mark F. Rooker, Dennis R. Cole Leviticus 2000 Page 108 "This latter category cannot be expiated, and the offender is karat, “cut off ,” a term often understood as designating a premature death"
- International Standard Bible Encyclopedia: E-J - Page 219 Geoffrey W. Bromiley - 1995 "Kerithoth (<Heb. karat, "to cut off"). Examples include breaking the fast on the Day of Atonement (Ex. 12:15-19), sexual violations, and ritual impurities (Lev. 18:6-30). "
- de Sola Pool, David (1916). Capital punishment among the Jews: a paper read before the New York Board of Jewish Ministers. Bloch. p. 26.
- Nachmanides, Commentary on the Torah. Leviticus 18:29
- Shaarie TeshuvaPart 3 Sec. 120
- Maimonides, Mishneh Torah, Laws of Repentance 8:1
- Nachmanides, Commentary on the Torah. Leviticus 18:29
- The Sabbath In Scripture - Page 83 Kareth (cutting off), often translated "extirpation," is a punishment often referred to in the Old Testament ("that soul shall be cut off from among his people"). Kerithoth 1:1 lists thirty-six transgressions for which ...
- Year book of the Central Conference of American Rabbis: Volume 27 Central Conference of American Rabbis - 1917 "There are thirty-six sins which are punishable by excision (Kareth), of which if a man transgress one of them, he is guilty of death; have I perhaps transgressed one of them? Why then do you bring death upon me?"
- Jacobs, Louis. "Karet (Spiritual Exile)". MyJewishLearning. Retrieved 15 April 2011.
- Mishnah Krithoth 1:1, interpretation according to Maimonides, Commentary on Mishnah, Krithoth 1:1
- Maimonides, Commentary on Mishnah, Krithoth 1:1
- Sherwood, Stephen K. (2002). Leviticus, Numbers, Deuteronomy. Liturgical Press.
- Etshalom, Yitzchak "Shabbat and Mikdash" Parashat Ki Tissa' 1995-2007' http://www.torah.org/advanced/mikra/5757/sh/dt.57.2.09.html# (2011)