Rambam - 1 Chapter a Day

Either he was unaware that the activity involved a transgression or that the transgression was punishable by karet or he knew that the activity was forbidden, but was unaware that he was performing that forbidden activity.

One is not obligated to bring such an offering for failing to fulfill positive commandments including even the positive commandments of bringing the Paschal sacrifice and circumcision whose omission is punishable by karet, as stated in the following halachah.

See the following halachah.
See the gloss of Rav Yosef Corcus who explains that even when it is possible that a prohibition be violated by the performance of a deed, but one violates it without performing a deed - e.g., one accepts a false deity as a god, which violates the prohibition against idolatry, but does not involve a deed - there is no obligation to bring a sin-offering.

Literally, the soul's being cut off. This involves premature death in this world (before the age of 50, Mo'ed Kattan 28a) and the soul not meriting a portion in the world to come (Hilchot Teshuvah 8:1).

Sefer HaMitzvot (positive commandment 69) and Sefer HaChinuch (mitzvah 121) include this commandment in the reckoning of the 613 mitzvot. The Ramban in his gloss to Sefer HaMitzvot (General Principle 12) mentions the opinion of Halachot Gedolot who interprets the mitzvah as being incumbent on the priests to offer the sacrifice rather than on the transgressor to bring it.

See Hilchot Avodat Kochavim 2:7 for details regarding this prohibition.

As the Rambam writes in the beginning of Hilchot Milah, this refers to a person who was not circumcised and not to a father who failed to circumcise his son.

See Hilchot Karban Pesach 1:2, 5:1.

This is the prooftext cited in the standard printed text of the Mishneh Torah. Several authentic manuscripts and the Rambam’s Commentary to the Mishnah cite Leviticus 4:13, which uses similar, but slightly different wording. We have chosen the version of the standard printed text, because the other verse does not refer to an individual sin-offering, but one brought by the Sanhedrin.

In this context, speech is not considered as an act.

If there were witnesses and a warning was given.

The prooftext from which the obligation to bring the sacrifice is derived.

In contrast to the Sanhedrin.

This term is used to differentiate the sacrifice from an adjustable guilt-offering which varies depending on the person's income, as explained in the following halachah.

I.e., the Temple Courtyard, as explained in Hilchot Bi’at HaMikdash 3:12.

Chapter 10, Halachot 1,5.

Two young doves or two turtle doves.

I.e., if he is very poor. See Chapter 10, Halachah 4.

Keritot 1:1 mentions “one who is intimate with a woman and her daughter.” The Rambam mentions more particulars because this category includes a woman and her mother, her maternal grandmother, her paternal grandmother, her daughter, her daughter’s daughter, and her son’s daughter (Lechem Mishneh).

Whether born out of marriage or out of wedlock.

This is speaking even about an instance where his father has not married the woman who gave birth to his sister. Similarly, it includes a maternal sister as well as a paternal sister.

In which instance, he is liable for two sin-offerings; see Hilchot Issurei Bi’ah 2:2-4.

I.e., during the lifetime of his wife. After she dies, her husband is permitted to marry her sister.

Even if she is not his mother.

I.e., during his brother’s lifetime or after his death, if he leaves children. If he does not leave children, he is obligated to marry his brother’s wife to fulfill the mitzvah of yibbum.

In which instance, he would be liable for two sin-offerings, one for violating this specific prohibition and one for violating the prohibition against being intimate with a male.

The details concerning these prohibitions are mentioned in Hilchot Issurei Bi’ah, chs. 1-2.

See Hilchot Avodat Kochavim, ch. 1.

In contrast to one who merely accepts a false deity as a god, as stated in Halachah 2 above.

A false divinity worshiped in Biblical times. See Hilchot Avodat Kochavim 6:3.

Ibid.: 1.

Ibid.:2. The Rambam mentions the performance of a deed, because generally, this prohibition is violated without performing a deed (Keritot 3b) in which instance, a sacrifice is not required.

Hilchot Shabbat 1:1, 7:1.

Hilchot Sh’vitat Asor 1:1.

Ibid.:4.

Hilchot Chametz UMatzah 1:1.

Hilchot Ma’achalot Assurot 7:1.

Ibid. 6:1.

Hilchot Pesulei HaMukdashim 18:10.

Ibid.:6.

Hilchot Hilchot Ma’aseh HaKorbanot 18:3.

Ibid.:2.

Used to anoint the High Priest, king, and vessels of the Sanctuary; see Hilchot K’lei HaMikdash 1:4.

Ibid. 2:9.

Ibid. 1:5.

Numbers 15:27.

See Deuteronomy, ch. 20; Hilchot Melachim 7:1.

In contrast to other transgressions, where there is a difference depending on the person’s standing.

Leviticus 4:27-31 with regard to a she-goat; ibid.:32-35 with regard to a ewe.

Ibid. 4:22-26.

This term includes both the High Priest and the priest anointed to lead the nation in war. After the anointment oil was entombed towards the end of the era of the First Temple, a High Priest was also not required to bring this sacrifice, because he had not been anointed (Hilchot K’lei HaMikdash 4:14).

See Leviticus 4:3-12.

One for eating on Yom Kippur and one for working on that holy day. Rav Yosef Corcus explains that this applies even if the two transgressions came about due to one lapse of awareness, i.e., the person did not know that the day was Yom Kippur.

We do not say that since the sin was committed by all the inhabitants of the city, one sin-offering is sufficient. Although there is a concept of communal sin-offerings, these involve transgressions performed because of an erroneous ruling by the Sanhedrin, as explained in Chapter 12.

The transgression against idolatry is mentioned, because it requires a different type of sacrifice than other transgressions, whether the transgression was committed by an individual or as a result of an erroneous ruling by the Sanhedrin.