The 7th day of Pesach is also a full-fledged Torah holiday. It celebrates the miracle of the Splitting of the Sea and our crossing on dry land (see first article).
The 2nd article, on the theme of miracles and redemption, is based on the haftorah reading of the Eighth Day of Pesach, celebrated only outside of Israel.
Between Pesach and Shavuot we "Count the Omer" - see article #3, plus more in the weeks to come.
Our 4th article presents mystical insights for the first chapter of Pirkei Avot (the mishnaic tractate of 'Ethical Principles'),
of which we study one chapter each Shabbat until Shavuot (and many repeat the cycle until Rosh Hashana).
A major theme of this week's reading, Shemini, is Eating Kosher — see the last three articles.