Rambam - 1 Chapter a Day

Sefer HaMitzvot (positive commandment 53) and Sefer HaChinuch (mitzvah 489) include this as one of 613 mitzvot. See Sefer HaMitzvot (General Principle 13) where the Rambam explains that the fact that the mitzvah is observed on three separate occasions does not cause it be considered as three separate mitzvot.

Sefer HaMitzvot (positive commandment 52) and Sefer HaChinuch (mitzvah 88) include this as one of 613 mitzvot.

Sefer HaMitzvot (positive commandment 54) and Sefer HaChinuch (mitzvah 488) include this as one of 613 mitzvot.

I.e., the first day of the three pilgrimage festivals: Pesach, Shavuot, and Sukkot. The laws applying to compensating for failure to bring the offering on the first day are mentioned in Halachot 4-8.

Young doves or turtle-doves. See the Kessef Mishneh and Rav Yosef Corcus who discuss this ruling, noting that seemingly, Chagigah 7a requires that these burnt-offerings be brought from domesticated animals and not from fowl. They suggest that the Rambam had a different version of that passage. The Or Sameach brings support for the Rambam’s ruling here from Hilchot Kiddush HaChodesh 4:7 which states that a leap year could be declared because of a lack of doves for the festival pilgrims. Why would the festive pilgrims need doves? For these burnt-offerings.

A goat, a sheep, or a bull.

Sefer HaMitzvot (negative commandment 156) and Sefer HaChinuch (mitzvah 490) include this prohibition as one of 613 mitzvot.

As stated in Hilchot Sanhedrin 18:2, one is only liable for lashes for violating a negative commandment that involves the performance of a deed.

And not from fowl. See Hilchot Ma’aseh HaKorbanot 1:11.

See more particulars in Chapter 2, Halachah 1. Women are not obligated in the observance of these mitzvot, because they are positive commandments whose observance is associated with a specific time and there is no specific verse teaching that women are obligated.

See also Hilchot Sh’vitat Yom Tov 6:17 which states: The “rejoicing” mentioned in the verse refers to sacrificing peace-offerings.... Nevertheless, [included in this charge] is that a person, his children, and the members of his household should rejoice, each one in a manner appropriate for him. In the following halachah in that source, the Rambam explains that each person should celebrate the festivals in a way which gives him natural satisfaction.

Although this prooftext is not referring to peace-offerings brought on festivals, it does teach us that rejoicing in God’s presence involves peace-offerings (Kessel Mishneh).

See Chagigah 6b and Rosh HaShanah 6b which interpret the term “your household,” in Deuteronomy 14:26: “And you shall rejoice, you and your household,” as referring to the person’s wife. The Ra’avad explains that although women are obligated to rejoice on the festivals, they are not obligated to bring sacrifices. Instead, her husband should bring her rejoicing. Rav Yosef Corcus states that one could interpret the Rambam’s words as meaning that a woman fulfills her obligation with her husband’s sacrifice, but the simple meaning is that there is an independent obligation incumbent upon her.

This applies both to the value of the sacrifice, as stated here, and also the number of sacrifices brought, as mentioned in Chapter 2, Halachah 6.

Implying that everything is dependent on the person’s generosity.

Equivalent to the weight of sixteen barley corns of pure silver [Commentary to the Mishnah (Chagigah 1:2)].

In his Commentary to the Mishnah (op. cit.), the Rambam explains that the peace-offerings must be more substantial, because in contrast, to the burnt-offerings which are consumed merely by the altar, the peace-offerings are consumed by the owners as well.

From Chagigah 1:5 (quoted in Halachah 11), it appears that the Rambam is referring to the continuation of the phrase: “According to the blessing of God your Lord which He granted you.”

We have translated kessef as “silver,” because of the contrast to gold mentioned tater on. It could, however, be translated as “money,” because the reason for the preference of silver is that it was the medium of exchange commonly used when trading in the marketplace.

According to Rabbinic decree.

We are concerned that he will conduct his transaction in haste and not realize that the money he received contains impurities. In contrast, if he brought money from home, it cart be assumed that he inspected it.

The Rambam does not mention the celebratory peace-offerings, because the mitzvah to bring them applies equally throughout the holiday (Rav Yosef Corcus).

From this concept, a parallel is derived with regard to the burnt-offerings.

For; as stated in Halachah I and the following halachah, the fundamental mitzvah is to bring these offerings on the first day of a holiday.

I.e., the sacrifices should be brought as soon as possible, without undue delay.

We have translated the verse according to its interpretation in Berachot 28a, the Rambam’s source. A literal translation would lead to a different meaning.

There are some authorities (see Turei Even to Chagigah 9a) who recommend bringing the sacrifices afterwards. as freewill offerings.

Although in some contexts Shemini Atzeret is considered as a separate holiday (see Sukkah 47a), in this context, it is still considered as part of Sukkot.

Chagigah 17a understands the fact that the three holidays are mentioned together in the same verse as an allusion to the concept that Shavuot is also granted days of compensation. Nevertheless, only six days of compensation are granted like Pesach, rather than seven like Sukkot; for the minimum - rather than the maximum - addition is made.

Though the Rambam does not mention the celebratory peace-offerings in this clause, everything stated applies to them as well.

Thus if the first day of the festival is the Sabbath or the majority of the people, priests, or sacrificial utensils are impure, the offering should not be brought.

Which are brought in such instances, as stated in Hilchot Bi’at HaMikdash 4:9-10.

In Halachot 4-7. Although it is preferable to bring the sacrifices on the first day, since it is not an absolute requirement, no leniency is granted in this instance.

And are offered on those days although there are prohibitions against performing labor.
There is a difference of opinion concerning this matter between the School of Shammai who rule that the offering of these sacrifices should also be postponed and the School of Hillel who rule that they should be offered. See Shulchan Aruch HaRav 494:19 which explains that since the burnt-offerings are offered entirely on the altar and not eaten by their owners, many people adopted the stringency suggested by the School of Shammai and did not offer them on a holiday. (Note similar statements by Tosafot Rid, Chagigah 18a.)
See also Likkutei Sichot, Shavuot, 5746, which explains that the stringency is associated particularly with the holiday of Shavuot and was instituted to emphasize how that holiday is a day of celebration for the Jewish people on the material plane.

See Hilchot Ma’aseh HaKorbanot 4:4-5 for an explanation of these two different types of sacrifices.

Since they are not associated with the holidays per se, and can be brought afterwards, there is no reason to allow them to be offered on the holiday itself (Beitzah 20b).

Which a person voluntarily commits himself to bring.

See Hilchot Ma’aseh HaKorbanot 3:6, 11, 13, which state that, generally, before offering a sacrifice, a person must lean on the sacrificial animal with all his might, placing both hands on its head. This act is called semichah.

Ibid.:12. Since it is not an indispensable element of offering the sacrifice, one might think that it would be forbidden, because generally, we are prohibited against making use of animals on the Sabbath and festivals (see Hilchot Shabbat 21:9).

The term shvut refers to a prohibition instituted because an activity resembles an activity forbidden on the Sabbath or might lead to the performance of such an activity (See Hilchot Shabbat 21:1).

There are certain restrictions against performing work on these intermediate days (Hilchot Sh’vitat Yom Tov 7:1). Nevertheless, based on the verse cited, our Sages (Beitzah 19b, Chagigah 7a) did not impose those restrictions in this instance.

The sacrifices mentioned previously in that Biblical passage.

To enable the members of his household to derive satisfaction from the festival.

As long as he brings the minimal measure, he fulfills his responsibility. There is no need to impoverish himself to bring these sacrifices.

To express his thanks to the Almighty.

Lest the sacrificial meat be left over beyond the required time and thus disqualified.

Chagigah 8b; see Halachah 2.