General Overview: This week's reading, Shemini, is a continuation of the previous week's reading, Tzav, where we learned about the Tabernacle's seven-day inaugural ceremony. This week's reading opens on the eighth day, when G‑d's presence descends upon the Tabernacle. On that day, Aaron's sons Nadab and Avihu die when offering an uncalled-for incense sacrifice. The portion concludes with a discussion about the laws of Kosher and ritual purity.
First Aliyah: Moses gathers all the Jews to the Tabernacle to witness the Divine presence descending upon the Sanctuary on that day. Aaron offers various sacrifices in preparation for this revelation.
Second Aliyah: After concluding the offering of all the sacrifices, Aaron blesses the people with the priestly blessing. Moses and Aaron bless the Jewish people that G‑d's presence dwell in their handiwork, and, indeed, the Divine presence visibly descends upon the Tabernacle.
Third Aliyah: At this point a heavenly fire descends and consumes the offerings on the altar. Aaron's eldest two sons, Nadab and Avihu, bring an unauthorized incense offering and a heavenly fire consumes them. Moses orders the removal of their bodies from the Tabernacle, and instructs Aaron and his remaining two sons not to observe the traditional laws of mourning, considering that they had to continue serving in the Sanctuary on behalf of the Jewish nation. The priests are instructed not to imbibe wine before performing Temple service.
Fourth Aliyah: Moses addresses Aaron and his sons, instructing them regarding the consumption of that day's offerings -- despite the deaths of their next of kin.
Fifth Aliyah: Moses becomes aware that one of the sin offerings had been burnt, rather than eaten. When he expresses his displeasure, Aaron explains his reasoning for ordering the burning of that particular offering, and Moses humbly accepts Aaron's explanation.
Sixth Aliyah: G‑d gives the commandments of Kosher, explaining how to distinguish between kosher and non-kosher animals, fish, and birds. Kosher animals must chew their cud and have cloven feet. The Torah lists four animals that have only one of these attributes, but not both, and are therefore non-kosher. Kosher fish must have fins and scales. The Torah then gives a list of species of non-kosher birds, and species of kosher locust. The Torah then discusses the ritual impurity caused by coming in contact with the carcass of a non-kosher animal, as well as certain species of rodents and amphibian creatures.
Seventh Aliyah: We learn of the possibility of foods and utensils contracting ritual impurity if they come in contact with any of the aforementioned impurities. The Torah then mentions the impurity contracted through coming in contact with the carcass of a kosher animal which was not ritually slaughtered. We are commanded not to consume any insects or reptiles. The reading closes with an exhortation that we remain holy by abstaining from eating all forbidden foods.