The first reference in the tanakh is in the story of Cain and Abel in Genesis chapter 4. Here it is clear that it is the motivation for the sacrifice that counts – Abel offered full-heartedly while Cain offered grudgingly because his brother had made an offering.
Noah made a sacrifice for thanksgiving – Genesis 8 – and it is recorded that "Noah was righteous among his generation". (Jewish scholars debate the two possible understandings of this statement.)
Abraham (Avraham), Isaac and Jacob all built altars for worship, but the rabbi points out that they only offered sacrifices on them where the tanakh says so. (Genesis 12 v8, 13 v18, and 33 v20 )
The sacrifice in Genesis 15 v7-81 was an exception. It was specifically the making of a covenant, and it was instigated by YHVH Himself. (See "The Miracle of the Scarlet Thread" by Richard Booker [Books])
The binding of Isaac (the Akedah) makes it clear that the sacrifice of Isaac was never God’s intention. Abraham knew God’s promise was to be fulfilled through Isaac, but he was being tested. (Genesis 22) (See also 2 Kings 3 v27 for reference to human sacrifice among Israel's pagan neighbours)
Jacob built an altar and offered sacrifice before leaving the land of Israel, knowing that he was not to offer sacrifice elsewhere. (Genesis 28 v20-22 - a stone set up as God's house (Biet El )
Prayer and , sometimes, sacrifice was the essence of the (private) worship of the patriarchs. This thread remains in Judaism – Essentially there are three types of prayer –
"Thank you God" – "Sorry God" – "Help me God"
Later on the communal service of Israel was developed in the Tabernacle and, later, the Temple. The sacrificial service had no liturgy; it stood alone. Early on, portions of scripture were used as prayer, most notably the Shema of Deuteronomy 6. Later on Psalm 100 was used with thanksgiving offerings, sung by the Levites.
To try and appreciate the sacrificial service one needs to imagine the impact on the individual coming to the Temple . . . .
The Temple was overawing – in its splendour, the presence of God and the knowledge that miracles happened there.
The sacrificial service was profoundly dramatic.
In the case of a sin or guilt offering, the slaughter of the animal in his stead and the splashing of its blood (life) would surely convince him not to do it again; whatever it was he had done.
The Cohanim testified that it was a deeply beautiful and meaningful service. This assertion may sound deeply strange to the twenty first century western man or woman, with our concern for animals and our removal from realities of food production. However, it is worth remembering that modern man is not in a strong position to condemn earlier ages for spilling blood. The twentieth century saw the Holocaust, the genocides in Rwanda and Armenia, Pol Pot’s Cambodia and Saddam Hussein’s Iraq. The world has watched most of these bloodbaths without doing too much about them. We are not in a position to evaluate animal sacrifice objectively, and thus judge God for instituting it.
There are three principles involved in Sacrifice
1 Sincerity of heart and devotion of mind – to lead the offerer to a higher level of devotion in his daily life; also, in the case of atonement, to instill contrition.
2 It is not the propitiation of an angry, bloodthirsty god who needed blood like the pagan gods did.
3 It replaced the human sacrifice which was practiced by the surrounding pagan nations (and by Israel in their times of apostasy). Consider also the Akedah mentioned earlier.
Also
The one offering the animal had to have first purchased it or have reared it – the sacrifice cost him something. Remember David refusing to accept the land to build an altar as a gift, saying, " I will not sacrifice to my God burnt offerings that cost me nothing." (2 Samuel 24 vs18-24)
Sacrifice was not God’s priority
When Saul and his army brought back animals to sacrifice, after having been instructed to destroy everything (1 Samuel 15) he was sternly rebuked, "Does ADONAI take as much pleasure in burnt offerings and sacrifices as in obeying what ADONAI says? Surely obeying is better than sacrifice and heeding orders than the fat of rams." For rebellion is like the sin of sorcery, stubbornness like the crime of idolatry. Because you have rejected the word of ADONAI, he too has rejected you as king."
Sacrifice is not a subject to be considered or practiced on its own – it must be part of sincerity and obedience – anything else is disgusting – see Hosea 6 (v6), Isaiah 1 (v11), Psalm 50 (v8), the last chapter of Isaiah and Jeremiah 7 (v21).
See 2 Chronicles 29 & 30 for an account of the worship, including sacrifice, which accompanied a major time of repentance and revival. Note especially ch29 v24, making atonement for all Israel and v30, they sang praise until they were filled with joy.
Sharing a meal with God
Except in the case of a burnt offering, which was totally burned on the altar, only a portion was burned. Another portion went to the priest and the rest went to the offerer to cook and eat in the Temple, in Jerusalem or within sight of the Temple. Thus one would be aware of sharing the offering as guests at His table – God is with us while we eat. Consider this aspect when pondering the offering of yourself as a living sacrifice (Romans 12) – many sacrifices involved giving over to God, but receiving back to share with God, with His blessing.
After 70AD (CE)
With the destruction of the Temple and the dispersion, all sacrificial service ceased. But the traditions are preserved in Judaism
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All services refer to sacrifices
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At festivals, the appropriate sacrificial service is read
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At Yom Kippur, the whole service is read
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The Seder represents the sacrifice and eating of the Passover lamb
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Reciting the scriptures replaces the actual sacrifice, and charitable acts and giving is practiced in place of providing the animal. Prayer and repentance must accompany the worship, as was always the case.
Blemished animals
For your benefit, you would never offer a less than perfect animal!
You must do your best when offering to God.
How do we know it is forbidden to shame someone in public?
See Leviticus 7, "In the place where you offer burnt offerings, there you offer guilt (or sin) offerings". There was no special place for guilt offerings, so you couldn’t tell that someone was making a guilt offering.
Sacrifice was never for God’s benefit.
It was for the spiritual advancement of the person making the offering
http://fp.thebeers.f9.co.uk/sacrifice.htm
Sacrifice in the Tanakh and in Jewish thought
http://fp.thebeers.f9.co.uk/sacrifice.htm