Leviticus 8 - Aaron and his sons are publicly ordained into the priesthood. They are dressed in the appropriate clothing, anointed with oil to symbolize their power and authority would come from the Spirit of God. A sin offering was presented on their behalf to remind them and the people as well that even these priests must be held accountable for their own sins. A second offering was presented to show the special hand of God on their lives as they served in the priestly ministry. Today, all believers are seen as priests before the Lord, 1 Peter 2:9.
Leviticus 9 - Aaron and his sons immediately entered into their priestly responsibilities. Once again, before they would offer the sin offering on behalf of the people they would offer their own sin offering. Then they would offer fellowship and grain offerings in obedience to God and in helped people to know a godly character brings a sweet "aroma" before the Lord. The Lord showed His approval of their offerings by sending fire from heaven. This caused the people to glorify Him for they knew He accepted their sacrifices.
Leviticus 10 - Here, again, is one of those chapters you wished you didn't have to read. Nadab and Abihu, sons of Aaron, and priests in their own right, brought before the Lord a "strange offering," perhaps incense of their own making. God was not at all pleased and immediately struck them dead in the Tabernacle. Later in this chapter God would warn the priests not to be influenced by alcohol before they attended to their duties. The implication is that this was Nadab and Abihu's sin which caused them to be reckless in their ministry. At the end of this chapter Moses expected Aaron to keep the "letter of the law" but Aaron was correct in keeping the "spirit of the law."