A major theme of this week's reading, Shemini, is Eating Kosher — see first 2 articles.
The ultimate goal of leaving Egypt was not just to escape slavery, but to forge the Torah Covenant at Sinai. There is a unique mitzvah for the seven weeks between the two holidays (article #3).
Our 4th article presents insights (as does the story—7th article) for the first chapter of Pirkei Avot (the Mishnaic tractate of 'Ethical Principles'), of which we study one chapter each Shabbat until Shavuot.
The Haforah is about King David, as is article #6 from a great Sephardic Kabbalist.
(Those of you in Israel should click to Tazria-Metzora for articles on their Weekly Reading.)