There are seven types of offerings:
1. Burnt offering: male without blemish, burnt with fire and causing sweet savour.
2. Free will offering
3. Sin offering: usually a goat, could be calf, 2 turtles or 2 pidgeons.
4. Trespass offering: like sin offering
5. Meat offering
6. Peace offering
7. Consecrations
Atonements were made by priests like Aaron, during sin offering. "And he said, Take now thy son, thine only [son] Isaac, whom thou lovest, and get thee into the land of Moriah; and offer him there for a burnt offering upon one of the mountains which I will tell thee of. And Abraham rose up early in the morning, and saddled his ass, and took two of his young men with him, and Isaac his son, and clave the wood for the burnt offering, and rose up, and went unto the place of which God had told him." (Genesis 22:2,3)
"And Abraham took the wood of the burnt offering, and laid [it] upon Isaac his son; and he took the fire in his hand, and a knife; and they went both of them together. And Isaac spake unto Abraham his father, and said, My father: and he said, Here [am] I, my son. And he said, Behold the fire and the wood: but where [is] the lamb for a burnt offering? And Abraham said, My son, God will provide himself a lamb for a
burnt offering: so they went both of them together." (Genesis 22:6,7,8)
"And Abraham lifted up his eyes, and looked, and behold behind [him] a ram caught in a thicket by his horns: and Abraham went and took the ram, and offered him up for a burnt offering in the stead of his son." (Genesis 22:13) "And Jethro, Moses' father in law, took a burnt offering and sacrifices for God: and Aaron came, and all the elders of Israel, to eat bread with Moses' father in law before God." (Exodus 18:12)
"And thou shalt burn the whole ram upon the altar: it [is] a burnt offering unto the LORD: it [is] a sweet savour, an offering made by fire unto the LORD." (Exodus 29:18)
And thou shalt receive them of their hands, and burn [them] upon the altar for a burnt offering, for a sweet savour before the LORD: it [is] an offering made by fire unto the LORD." (Exodus 29:25)
"[This shall be] a continual burnt offering throughout your generations [at] the door of the tabernacle of the congregation before the LORD: where I will meet you, to speak there unto thee. (Exodus 29:42) And thou shalt anoint the altar of the burnt offering, and all his vessels, and sanctify the altar: and it shall be an altar most holy. (Exodus 40:10) And he put the altar of burnt offering [by] the door of the tabernacle of the tent of the congregation, and offered upon it the burnt offering and the meat offering; as the LORD commanded Moses." (Exodus 40:29)
"If his offering [be] a burnt sacrifice of the herd, let him offer a male without blemish: he shall offer it of his own voluntary will at the door of the tabernacle of the congregation before the LORD. And he shall put his hand upon the head of the burnt offering; and it shall be accepted for him to make atonement for him. (Leviticus 1:3,4)
But his inwards and his legs shall he wash in water: and the priest shall burn all on the altar, [to be] a burnt sacrifice, an offering made by fire, of a sweet savour unto the LORD. And if his offering [be] of the flocks, [namely], of the sheep, or of the goats, for a burnt sacrifice; he shall bring it a male without blemish. (Leviticus 1:9,10)
"And he shall lay his hand upon the head of the goat, and kill it in the place where they kill the burnt offering before the LORD: it [is] a sin offering. And the priest shall take of the blood of the sin offering with his finger, and put [it] upon the horns of the altar of burnt offering, and shall pour out his blood at the bottom of the altar of burnt offering. (Leviticus 4:24, 25) And he shall lay his hand upon the head of the sin offering, and slay the sin offering in the place of the burnt offering. And the priest shall take of the blood thereof with his finger, and put [it] upon the horns of the altar of burnt offering, and shall pour out all the blood thereof at the bottom of the altar." (Leviticus 4:29,30)
"And he shall lay his hand upon the head of the sin offering, and slay it for a sin offering in the place where they kill the burnt offering. And the priest shall take of the blood of the sin offering with his finger, and put [it] upon the horns of the altar of burnt offering, and shall pour out all the blood thereof at the bottom of the altar: " (Leviticus 4:33,34) "And if he be not able to bring a lamb, then he shall bring for his trespass, which he hath committed, two turtledoves, or two young pigeons, unto the LORD; one for a sin offering, and the other for a burnt offering." (Leviticus 5:7)
" And he shall offer the second [for] a burnt offering, according to the manner: and the priest shall make an atonement for him for his sin which he hath sinned, and it shall be forgiven him." (Leviticus 5:10) "Command Aaron and his sons, saying, This [is] the law of the burnt offering: It [is] the burnt offering, because of the burning upon the altar all night unto the morning, and the fire of the altar shall be burning in it. And the priest shall put on his linen garment, and his linen breeches shall he put upon his flesh, and take up the ashes which the fire hath consumed with the burnt offering on the altar, and he shall put them beside the altar." (Leviticus 6:9,10)
"And the fire upon the altar shall be burning in it; it shall not be put out: and the priest shall burn wood on it every morning, and lay the burnt offering in order upon it; and he shall burn thereon the fat of the peace offerings." (Leviticus 6:12) Speak unto Aaron and to his sons, saying, This [is] the law of the sin offering: In the place where the burnt offering is killed shall the sin offering be killed before the LORD: it [is] most holy." (Leviticus 6:25)
"In the place where they kill the burnt offering shall they kill the trespass offering: and the blood thereof shall he sprinkle round about upon the altar." (Leviticus 7:2) This [is] the law of the burnt offering, of the meat offering, and of the sin offering, and of the trespass offering, and of the consecrations, and of the sacrifice of the peace offerings; (Leviticus 7:37) And he brought the ram for the burnt offering: and Aaron and his
sons laid their hands upon the head of the ram. (Leviticus 8:18) And he washed the inwards and the legs in water; and Moses burnt the whole ram upon the altar: it [was] a burnt sacrifice for a sweet savour, [and] an offering made by fire unto the LORD; as
the LORD commanded Moses." (Leviticus 8:21)
"And Moses took them from off their hands, and burnt [them] on the altar upon the burnt offering: they [were] consecrations for a sweet savour: it [is] an offering made by fire unto the LORD." (Leviticus 8:28) And he said unto Aaron, Take thee a young calf for a sin offering, and a ram for a burnt offering, without blemish, and offer [them] before the LORD." And unto the children of Israel thou shalt speak, saying, Take ye a kid of the goats for a sin offering; and a calf and a lamb, [both] of the first year, without blemish, for a burnt offering; " (Leviticus 9:2,3)
"And Moses said unto Aaron, Go unto the altar, and offer thy sin offering, and thy burnt offering, and make an atonement for thyself, and for the people: and offer the offering of the people, and make an atonement for them; as the LORD commanded.
(Leviticus 9:7) And he brought the burnt offering, and offered it according to the manner.
And he brought the meat offering, and took an handful thereof, and burnt [it] upon the altar, beside the burnt sacrifice of the morning." (Leviticus 9:16,17)
"And Aaron lifted up his hand toward the people, and blessed them, and came down from offering of the sin offering, and the burnt offering, and peace offerings. (Leviticus 9:22) And there came a fire out from before the LORD, and consumed upon the altar the burnt offering and the fat: [which] when all the people saw, they shouted, and fell on their faces. (Leviticus 9:24) And Aaron said unto Moses, Behold, this day have they offered their sin offering and their burnt offering before the LORD; and such things have befallen me: and [if] I had eaten the sin offering to day, should it have been accepted in the sight of the LORD?" (Leviticus 10:19)
"And when the days of her purifying are fulfilled, for a son, or for a daughter, she shall bring a lamb of the first year for a burnt offering, and a young pigeon, or a turtledove, for a sin offering, unto the door of the tabernacle of the congregation, unto the priest: (Leviticus 12:6) And if she be not able to bring a lamb, then she shall bring two turtles, or two young pigeons; the one for the burnt offering, and the other for a sin offering: and the priest shall make an atonement for her, and she shall be clean. (Leviticus 12:8)
"And he shall slay the lamb in the place where he shall kill the sin offering and the burnt offering, in the holy place: for as the sin offering [is] the priest's, [so is] the trespass offering: it [is] most holy: (Leviticus 14:13) And the priest shall offer the sin offering, and make an atonement for him that is to be cleansed from his uncleanness; and afterward he shall kill the burnt offering: (Leviticus 14:19) And the priest shall offer the burnt offering and the meat offering upon the altar: and the priest shall make an atonement for him, and he shall be clean." (Leviticus 14:20)
"And two turtledoves, or two young pigeons, such as he is able to get; and the one shall be a sin offering, and the other a burnt offering." (Leviticus 14:22) And the priest shall offer them, the one [for] a sin offering, and the other [for] a burnt offering; and the priest shall make an atonement for him before the LORD for his issue. (Leviticus 15:15)