"You shall present the Levites before Aaron and before his sons, and shall offer them as a wave offering to Jehovah" (v. 13). Aaron first offered the Levites to God as a wave offering before redemption (v. 11). Afterwards, Moses offered the sin offering and the burnt offering to make propitiation for the Levites. Then he presented them again before Aaron and his sons and offered them as a wave offering to Jehovah.
"Thus you shall separate the Levites from among the sons of Israel, and the Levites shall be Mine" (v. 14). Through the foregoing procedure, Moses separated the Levites from among the sons of Israel, and the Levites became God's.
The Lord took the Levites as the replacement of all the firstborn of the sons of Israel (v. 18). Therefore, the Levites went in to do the service of the tent of meeting instead of all the firstborn of the sons of Israel (vv. 15-18). If the Levites had not carried out this service, the firstborn of the sons of Israel would have been required to do it.
"I have given the Levites as ones given to Aaron and his sons from among the sons of Israel, to do the service of the sons of Israel in the tent of meeting, and to make propitiation for the sons of Israel, that there may be no plague among the sons of Israel when the sons of Israel approach the sanctuary" (v. 19). Here we see that God gave the Levites to Aaron, the head priest, and to his sons, the priests, to do the service in the tent of meeting and to make propitiation for the sons of Israel.