See Leviticus 3:1-17. What is here added, relates to the accompanying מנחה mı̂nchāh Leviticus 2:1, the classification of peace-offerings into:

(1) thank-offerings,

(2) vow-offerings and

(3) voluntary-offerings, and the conditions to be observed by the worshipper in eating the flesh.

And this is the law of the sacrifice of peace offerings, which ye shall offer unto the Lord. Some other laws and rules respecting the oblation of them: in Leviticus 3:1 an account is given of what they should be, both of the herd and flock, and of the burning of the fat of them; and here the several sorts of them are distinctly observed, what should be offered with them, and the part the priest should have of it, and when the flesh of them should be eaten.

The Law of the Peace-Offerings, "which he shall offer to Jehovah" (the subject is to be supplied from the verb), contains instructions, (1) as to the bloodless accompaniment to these sacrifices (Leviticus 7:12-14), (2) as to the eating of the flesh of the sacrifices (Leviticus 7:15-21), with the prohibition against eating fat and blood (Leviticus 7:22-27), and (3) as to Jehovah's share of these sacrifices (Leviticus 7:28-36). - In Leviticus 7:12 and Leviticus 7:16 three classes of shelamim are mentioned, which differ according to their occasion and design, viz., whether they were brought על־תּודה, upon the ground of praise, i.e., to praise God for blessings received or desired, or as vow-offerings, or thirdly, as freewill-offerings (Leviticus 7:16). To (lit., upon, in addition to) the sacrifice of thanksgiving (Leviticus 7:12, "sacrifice of thanksgiving of his peace-offerings," Leviticus 7:13 and Leviticus 7:15) they were to present "unleavened cakes kneaded with oil, and flat cakes anointed with oil (see at Leviticus 2:4), and roasted fine flour (see Leviticus 6:14) mixed as cakes with oil," i.e., cakes made of fine flour roasted with oil, and thoroughly kneaded with oil (on the construction, see Ges. 139, 2; Ewald 284 a). This last kind of cakes kneaded with oil is also called oil-bread-cake ("a cake of oiled bread," Leviticus 8:26; Exodus 29:23), or "cake unleavened, kneaded with oil" (Exodus 29:2), and probably differed from the former simply in the fact that it was more thoroughly saturated with oil, inasmuch as it was not only made of flour that had been mixed with oil in the kneading, but the flour itself was first of all roasted in oil, and then the dough was moistened still further with oil in the process of kneading.

And this is the law of the sacrifice of peace offerings, which he shall offer unto the LORD.

[1] peace-offerings

In the "law of the offerings," the peace-offering is taken out of its place as third of the sweet savour offerings, and placed alone, and after all the non-sweet savour offerings. The explanation is as simple as the fact is beautiful. In revealing the offerings Jehovah works from Himself out to the sinner. See Scofield Note: "Ex 25:10". The whole burnt-offering comes first as meeting what is due to the divine affections, and the trespass-offering last as meeting the simplest aspect of sin-- its injuriousness. But the sinner begins of necessity with that which lies nearest to a newly awakened conscience--a sense, namely, that because of sin he is at enmity with God. His first need, therefore, is peace with God. And that is precisely the Gospel order. Christ's first message is, "Peace" Jn 20:19 afterward He shows them His hands and His side. It is the order as 2Cor 5:18-21 first "the word of reconciliation," Lev 7:19, then the trespass- and sin-offering, Lev 7:21. Experience thus reverses the order of revelation.

11-14. this is the law of the sacrifice of peace offerings-Besides the usual accompaniments of other sacrifices, leavened bread was offered with the peace offerings, as a thanksgiving, such bread being common at feasts.

7:11-27 As to the peace-offerings, in the expression of their sense of mercy, God left them more at liberty, than in the expression of their sense of sin; that their sacrifices, being free-will offerings, might be the more acceptable, while, by obliging them to bring the sacrifices of atonement, God shows the necessity of the great Propitiation. The main reason why blood was forbidden of old, was because the Lord had appointed blood for an atonement. This use, being figurative, had its end in Christ, who by his death and blood-shedding caused the sacrifices to cease. Therefore this law is not now in force on believers.