ואלה תולדות אהרן ומשה ביום דבר ה' אל משה. At the time when G’d set the tribe of Levi apart from the other tribes, some of them having to transport the Tabernacle on its journeys, some to perform service in and around the Tabernacle and to pronounce blessings in G’d’s name. Nadav and Avihu were included in the people described as Levites.

ואלה שמות בני אהרן; each one of them was mentioned by his name, i.e. not only because he was a son of an illustrious father such as Aaron.

הכהנים המשוחים, future priests were not described in such terms as they were not anointed while the High Priest was alive. אשר מלא ידם לכהן, the reason why the sons of Aaron were also anointed with the oil of anointment was to enable them to perform priestly duties, as otherwise there would have been no priests other that Aaron, no one having been born as priest to a father who was a priest. Had they been born after Aaron’s appointment, they would not have required such anointing as heredity would have sufficed.

בהקריבם אש זרה, this was the only blemish they had been guilty of.

ובנים לא היו להם, if they had had sons, the sons would have been their replacements if they had been physically and mentally suitable.

ויכהן אלעזר ואיתמר, they had been given authority to substitute for their father in the Tabernacle if the need would arise, by the command of G’d.

על פני אהרן אביהם, during the lifetime of Aaron his sons had already been anointed. The death of two of them, as well as their replacing their father as High Priest was not at Aaron’s command, even though he was the High Priest. [if I understand the author correctly, he means that contrary to a king appointing a son as his successor, the High Priest is not entitled to appoint his own successor. Ed.] None of what is reported here is of significance for future generations as ordinary priests were not anointed, whereas the position of High Priest was not a position that could be inherited.

ושרתו אותו. Seeing that the ultimate responsibility for anything connected with the Tabernacle was Aaron’s, as we know from Numbers 18,1 אתה ובניך ובית אביך אתך תשאו את עון המקדש ואתה ובניך אתך תשאו את עון כהנתכם, “you and your sons and the house of your father with you will have to carry the sin or guilt of the Temple; and you and your sons with you will have to be responsible for any sin/guilt involving the priesthood you have been appointed to.” As a result of these verses, the service performed by the Levites was in the nature of being assistants to the priests, comprising standing guard over the Tabernacle, protecting it against the entry of people not in a fit state for one reason or another. They had to ensure that the vessels of the Tabernacle remained not only in good condition but were not stolen, etc. The second half of that verse in chapter 18 refers to no non-priests being allowed within the sacred domain reserved for either the priests or even only the High Priest.

משמרת כל העדה לפני אהל מועד לעבוד את עבודת המשכן, to assist in the tasks needed to perform the service in the Temple properly. Had it not been for the sin of the golden calf, it would have been the duty/privilege of the members of the Supreme Court, Sanhedrin, to carry out the tasks now allocated to the Levites.

משמרת בני ישראל לעבוד את עבודת המשכן, the auxiliary aspects of the service in the Tabernacle, to carry, to sing, etc; these tasks, if not for the sin of the golden calf, would have been assigned to ordinary members of the people at large instead of being reserved exclusively for the Levites.

נתונים נתונים המה לו, all their (the Levites’) service was to be performed at the instruction of Aaron, to whom the Levites had been delegated by the people.

מאת בני ישראל, who in turn obligated themselves to compensate their delegates, the Levites, by giving them the tithes of their crops.

ושמרו את כהנתם, concerning all matters involving the altar, the dividing curtain and what is beyond it, to ensure that the Levites not enter any of these domains.

והזר הקרב, any unauthorised person entering these domains will be legally executed (if he did it deliberately after due warning).

תחת כל בכור, as a redemption.

כי לי כל בכור, as the Temple service used to be the duty of the respective firstborn in each family.ביום הכותי כל בכור בארץ מצרים הקדשתי לי כל בכור בישראל, although at the time when the firstborn in Egypt were killed, the Jewish firstborn had been guilty of death also, as had been the firstborn of that entire generation. They were singled out for this penalty as they were the most honoured people of their time, and as such served as role models for others. There was no special merit due to which they would have been spared, as in Genesis 19,15 where the angels warned Lot not to remain in Sodom lest he too would be killed on account of the company he kept. G’d, in sanctifying them, i.e. placing them on a spiritually elevated pedestal so that they would not partake in all manner of secular pursuits, justified sparing them at that time. Now that, due to the sin of the golden calf, they had forfeited this spiritually elevated status, they had to be “redeemed” in order to resume life on a more mundane level than that for which they had been destined. This is the meaning of וכל בכור אדם תפדה, “you shall redeem every human male firstborn.” (Exodus 13,13). We must not make the mistake of thinking that seeing that this verse was written before the sin of the golden calf, that the firstborn had already been subject to redemption at that time, i.e that G’d had despised them as not fit to offer the sacrificial offerings. On the contrary, the “redemption” of which Exodus 13,13 speaks, i.e. [without a simultaneous substitution of others in their place, Ed.] was only in order to permit these firstborn to also pursue a regular lifestyle when they would not be performing service in the Temple, etc. Without “redemption” every object that has been sanctified is out of bounds for any mundane use whether passive or active, as it would constitute a demeaning of its holiness. (compare Chulin 137)

מאדם עד בהמה לי יהיו, from now on, humans have to be redeemed, animals to be slaughtered and their blood and fat offered on the altar.