The Torah portion is Shemini, Leviticus 9:1-11:47. In synagogues using the Triennial system, 5781 is year 2 and the Torah reading is Leviticus 10:12-11:32.
This parshah speaks of the offerings on the eighth day, that is, the day after the seven days of consecration of Aaron and the other priests. But it also speaks of the unauthorized offerings of Aaron's sons, Nadav and Abihu, who offered "strange" fire and were themselves consumed by fire. Aaron and his surviving sons were told not to observe normal mourning rituals for Nadav and Abihu. It goes on to speak of offerings that are normally eaten by the priests. It lays out the rules of kosher meat, fish, birds and other species, and other rules about kosher food.The haftarah is II Samuel 6:1-7:17. Like the Torah portion, this passage speaks of someone who was punished for improper behavior with a holy object, in this case Uzzah, who took hold of The Ark when oxen stumbled.
In synagogues using the Sephardic tradition, the Haftarah is II Samuel 6:1-6:19.