Melchizedek, priest and king
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Now this Melchizedek—king of Salem, priest of God Most High, who met Abraham returning from the slaughter of the kings and blessed him, to whom also Abraham gave a tenth part of all (first, his name means ‘king of righteousness’, and then again ‘king of Salem’, which means ‘king of peace’), without father, without mother, without genealogy; having neither beginning of days nor end of life, but having been made like the Son of God*One wonders if Melchizedek was not some sort of theophany, perhaps Jehovah the Son, Himself.—remains a priest continually.
Melchizedek greater than Abraham
Now consider how great this personage was, to whom even the patriarch Abraham gave a tenth of the spoils:Why would Abraham give a tenth of the spoils to a stranger? Something about Melchizedek was very impressive. When Jehovah the Son appeared to Abraham to announce the destruction of Sodom, he knew who He was. You see, those of the sons of Levi who receive the priesthood have a command, according to the Law, to collect a tithe from the people—that is, from their brothers—even though they too came out of Abraham's body; but he whose descent is not counted among them collected a tithe from Abraham and blessed him who had the promises. Now without dispute the lesser is blessed by the greater. Also, here men who die receive tithes, but there he of whom it is testified that he lives —in a word, even Levi, who receives tithes, paid the tithe through Abraham, 10 because he was still in the reproductive system of his forefather when Melchizedek met him.This is instructive. The inspired author affirms that Levi was in Abraham and also paid the tithe to Melchizedek, but when Abraham met Melchizedek not even Isaac had been born yet, much less Jacob and Levi. So the human spirit, the ‘image’ of the Creator, is transmitted by the male sperm. This agrees with Romans 5:12-21, where we are informed that Adam's sin contaminated all his descendants. When Eve sinned, she sinned alone. When Adam sinned, we did too.
Melchizedek greater than Aaron
11 Now then, if there could be perfection through the Levitical priesthood (for on the basis of it the people had received the Law), what further need would there be for a different kind of priest to arise according to the order of Melchizedek, rather than being called according to the order of Aaron? 12 (Because when the priesthood is changed there is also a change of law, of necessity.) 13 For He of whom these things are said belongs to a different tribe, from which no one has officiated at the altar. 14 For it is evident that our Lord arose out of Judah, of which tribe Moses spoke nothing concerning priesthood. 15 And it all becomes clearer still if a different kind of priest, in the likeness of Melchizedek, appears, 16 who has come, not on the basis of a law about a physical rule but on the basis of the power of an indestructible life.§“An indestructible life”—that is how come He can be “a priest forever”. 17 Because He testifies:
“You are a priest forever
according to the order of Melchizedek.”
18 You see, there is an annulling of the former rule because of its weakness and uselessness 19 (for the Law made nothing perfect), and a bringing in of a better hope, through which we draw near to God.
Our eternal High Priest represents us eternally
20 Further, inasmuch as it was not without the taking of an oath 21 —they indeed had become priests without an oath-taking, but He[S] with an oath by Him[F] who said to Him[S]:
“The Lord has sworn and will not change His[F] mind;
you are a priest forever
according to the order of Melchizedek”*Some 2% of the Greek manuscripts, of objectively inferior quality, omit “according to the order of Melchizedek” (as in NIV, NASB, LB, TEV, etc.).
22 —by so much Jesus has become the guarantee of a better covenant. 23 Also, there have been many priests because death prevented them from continuing in office; 24 while He[S], because He continues forever, has an unchangeable priesthood. 25 Therefore He is able to save absolutelyWonderful! He is always ‘there’ for us. those who come to God through Him, since He always lives and can intercede on their behalf.
26 Now such a High Priest was fitting for us—holy, innocent, undefiled, having been set apart from sinners, and having become higher than the heavens— 27 who, unlike those high priests, does not need to offer up daily sacrifices, first for His own sins and then for the sins of the people; because He did this once for all when He offered up Himself. 28 The Law appoints as high priest men who have weakness, but the word of the oath, that came after the Law, appointed Son, forever perfect.The Text has, literally, ‘having been perfected’ (or ‘completed’, or ‘consecrated’); the result of ‘having been perfected’ is to be perfect, and it is the result that is eternal, not the process.

*7:3 One wonders if Melchizedek was not some sort of theophany, perhaps Jehovah the Son, Himself.

7:4 Why would Abraham give a tenth of the spoils to a stranger? Something about Melchizedek was very impressive. When Jehovah the Son appeared to Abraham to announce the destruction of Sodom, he knew who He was.

7:10 This is instructive. The inspired author affirms that Levi was in Abraham and also paid the tithe to Melchizedek, but when Abraham met Melchizedek not even Isaac had been born yet, much less Jacob and Levi. So the human spirit, the ‘image’ of the Creator, is transmitted by the male sperm. This agrees with Romans 5:12-21, where we are informed that Adam's sin contaminated all his descendants. When Eve sinned, she sinned alone. When Adam sinned, we did too.

§7:16 “An indestructible life”—that is how come He can be “a priest forever”.

*7:21 Some 2% of the Greek manuscripts, of objectively inferior quality, omit “according to the order of Melchizedek” (as in NIV, NASB, LB, TEV, etc.).

7:25 Wonderful! He is always ‘there’ for us.

7:28 The Text has, literally, ‘having been perfected’ (or ‘completed’, or ‘consecrated’); the result of ‘having been perfected’ is to be perfect, and it is the result that is eternal, not the process.