The Torah portion is Shemini, Leviticus 9:1-11:47. In synagogues using the Triennial system, 5784 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.There is a special maftir portion (the final piece of the Torah reading) for Shabbat Ha-Chodesh: Exodus 12:1-20. Identifies "this month," the month of the Exodus now known as Nissan, as the first month of the year and speaks of the Pesach offering and the coming Plague of the Firstborn and the festival of Pesach (Passover).
The haftarah is for Shabbat Ha-Chodesh, Ezekiel 45:16-46:18. Speaks of the offerings and preparations for Pesach (Passover), which is coming soon!
In synagogues using the Sephardic tradition, the Haftarah is Ezekiel 45:16-46:15.