Tzav: the sacrificial system
1א

The entire Pentateuch (the five Mosaic books) forms a chiasmus. From the perspective of the Israelites in the wilderness, Bereishith looks back to the pre-history of Israel, while Devarim turns to the future, as Moses’ prophetic vision scans the far horizons of hope and expectation. Shemot and Bamidbar are a matched pair, telling the story of the present – Israel’s journey from Egypt into the desert and to the brink of the promised land.

This leaves Vayikra as the central and therefore the most important book (not by accident was it the Jewish custom for many centuries to begin teaching Torah to children by starting with Vayikra). At the centre of Vayikra itself is the so-called “holiness code”, chapter 19, with its great injunction, “Be holy, for I, the Eternal your God, am holy.” Vayikra is largely about sacrifices and the service of the priests. Hence its ancient name, Torat Kohanim, “the law of the priests,” from which we get the Latin-English word Leviticus (“of priestly matters”) (Jonathan Sacks)

2ב
(א) וַיִּקְרָ֖א אֶל־מֹשֶׁ֑ה וַיְדַבֵּ֤ר יְהוָה֙ אֵלָ֔יו מֵאֹ֥הֶל מוֹעֵ֖ד לֵאמֹֽר׃ (ב) דַּבֵּ֞ר אֶל־בְּנֵ֤י יִשְׂרָאֵל֙ וְאָמַרְתָּ֣ אֲלֵהֶ֔ם אָדָ֗ם כִּֽי־יַקְרִ֥יב מִכֶּ֛ם קָרְבָּ֖ן לַֽיהוָ֑ה מִן־הַבְּהֵמָ֗ה מִן־הַבָּקָר֙ וּמִן־הַצֹּ֔אן תַּקְרִ֖יבוּ אֶת־קָרְבַּנְכֶֽם׃

(1) The Eternal called to Moses and spoke to him from the Tent of Meeting, saying: (2) Speak to the Israelite people, and say to them: When any of you presents an offering of cattle to the Eternal, he shall choose his offering from the herd or from the flock.

3ג

Adam ki yakriv mikem korban l'Adonai - what does it mean? What can it mean?

4ד

Purposes of korbanot

Contrary to popular belief, the purpose of korbanot is not simply to obtain forgiveness from sin. Although many korbanot have the effect of expiating sins, there are many other purposes for bringing then and the expiatory effect is often incidental, and is subject to significant limitations.

The purposes of korbanot are much the same as the purposes of prayer: we bring qorbanot to praise God to become closer to God, to express thanks to God, love or gratitude. We bring them to celebrate holidays and festivals. Others are used to cleanse a person of ritual impurity (which does not necessarily have anything to do with sin: childbirth causes such impurity, but is certainly not a sin). And yes, many korbanot, like many prayers, are brought for purposes of atonement.

The atoning aspect of korbanot is limited. For the most part, korbanot only expiate unintentional sins, that is, sins committed because a person forgot that this thing was a sin. No atonement is needed for violations committed under duress or through lack of knowledge, and for the most part, korbanot cannot atone for a malicious, deliberate sin. In addition, they have no expiating effect unless the person making the offering sincerely repents his or her actions before making the offering, and makes restitution to any person who was harmed by the violation.

Major Types of Korbanot

Olah: Burnt Offering

Perhaps the best-known class of offerings is the burnt offering. It was the oldest and commonest sacrifice, and represented submission to God's will. The Hebrew word for burnt offering is olah meaning ascension. An olah is completely burnt on the outer altar; no part of it is eaten by anyone. Because the offering represents complete submission to God's will, the entire offering is given to God (i.e., it cannot be used after it is burnt). It expresses a desire to commune with God, and expiates sins incidentally in the process (because how can you commune with God if you are tainted with sins?). An olah could be made from cattle, sheep, goats, or even birds, depending on the offerer's means.

Zevach Sh'lamim: Peace Offering

A peace offering is an offering expressing thanks or gratitude to God.. The Hebrew term for this type of offering is zevach sh'lamim (or sometimes just sh'lamim), which is related to the word shalom, meaning "peace" or "whole." A representative portion of the offering is burnt on the altar, a portion is given to the kohanim, and the rest is eaten by the offerer and his family; thus, everyone gets a part of this offering. This category of offerings includes thanksgiving-offerings, free will-offerings, and offerings made after fulfillment of a vow. Note that this class of offerings has nothing to do with sin; in fact, the Talmud states that in the age of the messiah (when there is no more sin), this will be the only class of offering that is brought to the Temple.

Chatat: Sin Offering

A sin offering is an offering to atone for and purge a sin. It is an expression of sorrow for the error and a desire to be reconciled with God. The Hebrew term for this type of offering is chatat, from the word chayt, meaning "missing the mark." A chatat could only be offered for unintentional sins committed through carelessness, not for intentional, malicious sins. The size of the offering varied according to the nature of the sin and the financial means of the sinner. Some chatatot are individual and some are communal. Communal offerings represent the interdependence of the community, and the fact that we are all responsible for each others' sins. A few special chatatot could not be eaten, but for the most part, for the average person's personal sin, the chatat was eaten by the kohanim.

Asham: Guilt Offering

A guilt offering is an offering to atone for sins of stealing things from the altar, for when you are not sure whether you have committed a sin or what sin you have committed, or for breach of trust. The Hebrew word for a guilt offering is asham. When there was doubt as to whether a person committed a sin, the person would make an asham, rather than a chatat, because bringing a chatat would constitute admission of the sin, and the person would have to be punished for it. If a person brought an asham and later discovered that he had in fact committed the sin, he would have to bring a chatat at that time. An asham was eaten by the kohanim.

Food and Drink Offerings

A meal offering (minchah) represented the devotion of the fruits of our work to God, because it was not a natural product, but something created through human effort. A representative piece of the offering was burnt on the fire of the altar, but the rest was eaten by the kohanim.

There are also offerings of undiluted wine, referred to as nesekh

(taken from Judaism 101 jewfaq.org)

5ה
(כא) שָׂנֵ֥אתִי מָאַ֖סְתִּי חַגֵּיכֶ֑ם וְלֹ֥א אָרִ֖יחַ בְּעַצְּרֹֽתֵיכֶֽם׃ (כב) כִּ֣י אִם־תַּעֲלוּ־לִ֥י עֹל֛וֹת וּמִנְחֹתֵיכֶ֖ם לֹ֣א אֶרְצֶ֑ה וְשֶׁ֥לֶם מְרִיאֵיכֶ֖ם לֹ֥א אַבִּֽיט׃ (כג) הָסֵ֥ר מֵעָלַ֖י הֲמ֣וֹן שִׁרֶ֑יךָ וְזִמְרַ֥ת נְבָלֶ֖יךָ לֹ֥א אֶשְׁמָֽע׃ (כד) וְיִגַּ֥ל כַּמַּ֖יִם מִשְׁפָּ֑ט וּצְדָקָ֖ה כְּנַ֥חַל אֵיתָֽן׃ (כה) הַזְּבָחִ֨ים וּמִנְחָ֜ה הִֽגַּשְׁתֶּם־לִ֧י בַמִּדְבָּ֛ר אַרְבָּעִ֥ים שָׁנָ֖ה בֵּ֥ית יִשְׂרָאֵֽל׃
(21) I loathe, I spurn your festivals, I am not appeased by your solemn assemblies. (22) If you offer Me burnt offerings—or your meal offerings— I will not accept them; I will pay no heed To your gifts of fatlings. (23) Spare Me the sound of your hymns, And let Me not hear the music of your lutes. (24) But let justice well up like water, Righteousness like an unfailing stream. (25) Did you offer sacrifice and oblation to Me Those forty years in the wilderness, O House of Israel?
6ו
(כב) כִּ֠י לֹֽא־דִבַּ֤רְתִּי אֶת־אֲבֽוֹתֵיכֶם֙ וְלֹ֣א צִוִּיתִ֔ים בְּי֛וֹם הוציא [הוֹצִיאִ֥י] אוֹתָ֖ם מֵאֶ֣רֶץ מִצְרָ֑יִם עַל־דִּבְרֵ֥י עוֹלָ֖ה וָזָֽבַח׃ (כג) כִּ֣י אִֽם־אֶת־הַדָּבָ֣ר הַ֠זֶּה צִוִּ֨יתִי אוֹתָ֤ם לֵאמֹר֙ שִׁמְע֣וּ בְקוֹלִ֔י וְהָיִ֤יתִי לָכֶם֙ לֵֽאלֹהִ֔ים וְאַתֶּ֖ם תִּֽהְיוּ־לִ֣י לְעָ֑ם וַהֲלַכְתֶּ֗ם בְּכָל־הַדֶּ֙רֶךְ֙ אֲשֶׁ֣ר אֲצַוֶּ֣ה אֶתְכֶ֔ם לְמַ֖עַן יִיטַ֥ב לָכֶֽם׃ (כד) וְלֹ֤א שָֽׁמְעוּ֙ וְלֹֽא־הִטּ֣וּ אֶת־אָזְנָ֔ם וַיֵּֽלְכוּ֙ בְּמֹ֣עֵצ֔וֹת בִּשְׁרִר֖וּת לִבָּ֣ם הָרָ֑ע וַיִּהְי֥וּ לְאָח֖וֹר וְלֹ֥א לְפָנִֽים׃
(22) For when I freed your fathers from the land of Egypt, I did not speak with them or command them concerning burnt offerings or sacrifice. (23) But this is what I commanded them: Do My bidding, that I may be your God and you may be My people; walk only in the way that I enjoin upon you, that it may go well with you. (24) Yet they did not listen or give ear; they followed their own counsels, the willfulness of their evil hearts. They have gone backward, not forward,
7ז

What does Jeremiah mean? Did sacrifice really not figure in the leaving of Egypt and the desert?

8ח

. אָמַר רַבִּי יְהוֹשֻׁעַ, שָׁמַעְתִּי, שֶׁמַּקְרִיבִין אַף עַל פִּי שֶׁאֵין בַּיִת, וְאוֹכְלִים קָדְשֵׁי קָדָשִׁים אַף עַל פִּי שֶׁאֵין קְלָעִים, קָדָשִׁים קַלִּים וּמַעֲשֵׂר שֵׁנִי, אַף עַל פִּי שֶׁאֵין חוֹמָה, שֶׁקְּדֻשָּׁה רִאשׁוֹנָה קִדְּשָׁה לִשְׁעָתָהּ וְקִדְּשָׁה לֶעָתִיד לָבֹא:

(6) Rabbi Yehoshua said: I heard that we may sacrifice even without the Temple and eat the holy sacrifices even though there are no curtains, and [eat] the regular sacrifices and second tithes even though there is no wall [surrounding Jerusalem] because the first sanctification sanctified [the area] for its time and for the time to come.

9ט

It was possible to offer sacrifices even if the Temple was not there - why did the end of the temple mean the end of the sacrificial system?

10י
after the Tabernacle was destroyed, there is permission to sacrifice offerings on improvised altars. But with regard to the sanctity of Jerusalem, after the Temple was destroyed, there is no permission to sacrifice offerings on improvised altars, as the prohibition remains intact.
GEMARA: Rabbi Yitzḥak said: I heard that one sacrifices offerings in the temple of Onias in Egypt at the present time. The Gemara cites the basis for the statement of Rabbi Yitzḥak. He maintains that the temple of Onias is not a house of idol worship but rather a temple devoted to the service of God, and he maintains that the initial consecration sanctified Jerusalem for its time and did not sanctify Jerusalem forever. Therefore, after the destruction of the Temple, the sanctity of Jerusalem lapsed and the sacrifice of offerings elsewhere was no longer prohibited. For these reasons it was permitted to sacrifice offerings in the temple of Onias after the Temple was destroyed.
The Gemara cites the source of this halakha. It is as it is written: “For you are not as yet come to the rest and to the inheritance” (Deuteronomy 12:9), which is interpreted: “Rest,” this is Shiloh; “inheritance,” this is Jerusalem. The verse juxtaposes and likens inheritance to rest: Just as in the place of rest, Shiloh, after its destruction there is permission to sacrifice offerings on improvised altars, so too in the place of inheritance, Jerusalem, after its destruction there is permission to sacrifice offerings on improvised altars. BT Megillah 10a
11יא

ONIAS, TEMPLE OF, temple of the Hellenistic and Roman period established in Egypt for Jewish worship and sacrifice. Its location is given by Josephus as being in the district of Heliopolis, where it was built over an earlier ruined temple to Bubastis, the lioness-goddess; hence the area's other name Leontopolis. It was established for the worship of "God the most High," as that at Jerusalem (Ant., 13:62–68). The location is presumed to be at Tel el-Yehudiyah (Mound of the Jewess). .. It was destroyed in 73 C.E. on the orders of Titus or Vespasian (ibid., 421), who feared that it might become the focus of further revolt after the destruction of the Temple of Jerusalem in 70 C.E. At the earliest it could have been built in 170 B.C.E., shortly before the Hasmonean Revolt, because it is always referred to as the Temple of Onias (Ḥonia in Hebrew). There are two candidates for that honor, *Onias III (son of Simon II, the Just), who was high priest some time after 200 B.C.E., or his son *Onias IV. It is generally accepted that the earlier Onias, who was ousted by his Hellenizing brother Jason, was murdered in Antioch (II Macc. 4:34), so Onias IV is the more likely candidate. When he saw that his legitimate right to the High Priesthood had been usurped by the Hellenistic party, friendly to the Seleucids, Onias set up a rival sanctuary in Egypt, under the protection of their enemies, the Ptolemies.

12יב

"Granted now that the Roman destruction of the Temple terminated the sacrifices in a de facto way, the lack of some effort at reinstitution must rest on factors beyond merely the destruction...if sacrifices in the past were not impeded by the unavailablity of the Jerusalem Temple or other central sacnctuary, then why did not alnalogous or similar factors operate after 70?

13יג

The Sages taught in a baraita: There was an incident involving one High Priest who exited the Holy Temple and everyone followed him. When they saw Shemaya and Avtalyon, the heads of the Sanhedrin, walking along, in deference to them they left the High Priest by himself and walked after Shemaya and Avtalyon. Eventually, Shemaya and Avtalyon came to take leave of the High Priest before returning to their homes. Envious of the attention they received, he angrily said to them: Let the descendants of the gentile nations come in peace. Shemaya and Avtalyon descended from converts, and he scornfully drew attention to that fact. They said to him: Let the descendants of the gentile nations come in peace, who perform the acts of Aaron, who loved and pursued peace; and let not a descendant of Aaron come in peace, who does not perform the acts of Aaron and who speaks condescendingly to descendants of converts. (BT Yoma 71a-b)

14יד

"Rivalry betwen the High Priest and his aristocratic circle, and the Pharisaic leadershp had been ongoing for many years. It ceased wihen the Nasi became hereditary with the establishment of Hillel's line, and the dynastic Nesi'im moved up economically and socialy.. the Nasi became the defact leader of the Jewish people.... since the appointment of the High Priest was not in the hands of the Phjarisses, theyhad to content themselves that .. he complied with the Parasaic interpretation of the law, and even to coerce him if necessary. ..Among the Pharasiac leaders the most ardent opponent of the Sadducees and priests in general was Yohanan ben Zakkai, the Av Beit Din of the Pharasaic Sanhedrin, headed by Simon son of Gamliel 1. While Simon refrained from disputations with the Sadducees and politically even sought and gained their cooperation..his deputy Yohanan ben Zakkai did the opposite. He opposed the war against the Romans while fighting the Saducees and his political foresight made him the logical choice of Nasi after the war, when the Hillelilte dynasty became persona non grata because of their involvement. His strong and wise leadership was the principal reason for a smooth transition from a Temple centered sacrificial cult to a modified religion without Temple and sacrifice....He did not make the slightest effort to renew the sacrificial cult (as had been done before) ...he did not want to revive his adversaries. Buchler points out that of the fourteen sages who related matters which they saw in the Temple, only one was Yohanan's steady disciple in Yavneh - the others were not part of his school. It is also noteworthy that Yohanan in contrast to most Tannaim, does not care to relate tradtions or to discuss matters pertaining to sacrifices...While according to a tradtion in Avot de Rabbi Natan, Yohanan cried at the sight of the burning Temple, later he comforted Joshua ben Hananiah (his priestly disiciple) that we now have a way of atonement which is just as effective as sacrifices -gemilut hasadim, deeds of loving kindness. (Alexander Guttman, the End of the Jewish Sacrificial Cult)

15טו

"we may say that the destruction of the Temple was only one of three causes for the termination of the sacrificial cult. A second was the reluctance of the rabbinic leadership to revive the power of the priestly caste. A third was the change in the policy of the Romans who, having experienced a major disappointment when their appointee High Priests proved to be worthless to them when they needed them in 66CE , thereafter appointed no more High Priests. (Alexander Guttman ad loc)

16טז

God gave us the korbanot in order to wean us away from the idolatrous practices of the heathen nations in
which we had lived. God therefore redirected the sacrificial urge to God, and commanded us to offer sacrifices to God, so as to uproot the erroneous views we had acquired.

. . . the sacrificial service is not the primary object . . . supplications, prayers, and similar kinds of worship are nearer to the primary object, and indispensable for obtaining it . . . Now God sent Moses to make a kingdom of priests and a holy nation by means of the knowledge of God . . . The Israelites were commanded to devote themselves to God's service; compare ". . . and to serve God with all your heart."....

"When the Israelites received torah, the nations around them worhsipped images or the stars through sacrifices and the burning of incense in temples, and these were the religious rites with which the Israelites were familiar. It is a law of human nature that people resist being violently wrenched away from the forms in which they have been brought up. Prohibiting sacrifice outright and immediately instituting a more intellectual mode of worship would have been too great a shock. To wean the children of Israel away from the worship of images and stars and to turn their hearts towards the true God the Torah instructs them to build a sanctuary and an altar, to establish an elaborate system of sacrifices, and to install a priestly class, with the critical provso that everything be done for the sake of God"

(Maimonides excerpted from moreh nevuchim)